{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# INSTRUCTIONS\n",
    "\n",
    "#### Part 1: Computing the optimal speed from the optimal racing line\n",
    "- Part 1 of this notebook takes the optimal racing line, which can be generated with Race-Line-Calculation.ipynb ([GitHub](https://github.com/cdthompson/deepracer-k1999-race-lines)), and generates the optimal speed for each point on the racing line\n",
    "- Input: .py file with 2D array containing optimal racing line: 2 columns (x,y)\n",
    "- Output: .py file with 2D array: 4 columns (x,y,speed,expected time). This array can be inserted into the reward function\n",
    "- Note: The last point of the racing line is deleted because it is the same point as the first one\n",
    "\n",
    "#### Part 2: Computing the Action Space\n",
    "- Part 2 of this notebook takes the optimal racing line and speed, and uses K-Means with Gaussian Noise infused data, to calculate the action space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "import math\n",
    "\n",
    "# Ignore deprecation warnings we have no power over\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Path of the optimal racing line (.npy file)\n",
    "fpath = \"Spain_racing_line.npy\"\n",
    "\n",
    "# Change manually (this is only so that output files are named correctly)\n",
    "TRACK_NAME = \"Spain\"\n",
    "\n",
    "racing_track = np.load(fpath)\n",
    "\n",
    "# Convert np array to list and remove last point because it is the same point as the first one\n",
    "racing_track = racing_track.tolist()[:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Helper functions for Part 1 and Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uses previous and next coords to calculate the radius of the curve\n",
    "# so you need to pass a list with form [[x1,y1],[x2,y2],[x3,y3]]\n",
    "# Input 3 coords [[x1,y1],[x2,y2],[x3,y3]]\n",
    "def circle_radius(coords):\n",
    "\n",
    "    # Flatten the list and assign to variables (makes code easier to read later)\n",
    "    x1, y1, x2, y2, x3, y3 = [i for sub in coords for i in sub]\n",
    "\n",
    "    a = x1*(y2-y3) - y1*(x2-x3) + x2*y3 - x3*y2\n",
    "    b = (x1**2+y1**2)*(y3-y2) + (x2**2+y2**2)*(y1-y3) + (x3**2+y3**2)*(y2-y1)\n",
    "    c = (x1**2+y1**2)*(x2-x3) + (x2**2+y2**2)*(x3-x1) + (x3**2+y3**2)*(x1-x2)\n",
    "    d = (x1**2+y1**2)*(x3*y2-x2*y3) + (x2**2+y2**2) * \\\n",
    "        (x1*y3-x3*y1) + (x3**2+y3**2)*(x2*y1-x1*y2)\n",
    "\n",
    "    # In case a is zero (so radius is infinity)\n",
    "    try:\n",
    "        r = abs((b**2+c**2-4*a*d) / abs(4*a**2)) ** 0.5\n",
    "    except:\n",
    "        r = 999\n",
    "\n",
    "    return r\n",
    "\n",
    "\n",
    "# Returns indexes of next index and index+lookfront\n",
    "# We need this to calculate the radius for next track section.\n",
    "def circle_indexes(mylist, index_car, add_index_1=0, add_index_2=0):\n",
    "\n",
    "    list_len = len(mylist)\n",
    "\n",
    "    # if index >= list_len:\n",
    "    #     raise ValueError(\"Index out of range in circle_indexes()\")\n",
    "\n",
    "    # Use modulo to consider that track is cyclical\n",
    "    index_1 = (index_car + add_index_1) % list_len\n",
    "    index_2 = (index_car + add_index_2) % list_len\n",
    "\n",
    "    return [index_car, index_1, index_2]\n",
    "\n",
    "\n",
    "def optimal_velocity(track, min_speed, max_speed, look_ahead_points):\n",
    "\n",
    "    # Calculate the radius for every point of the track\n",
    "    radius = []\n",
    "    for i in range(len(track)):\n",
    "        indexes = circle_indexes(track, i, add_index_1=-1, add_index_2=1)\n",
    "        coords = [track[indexes[0]],\n",
    "                  track[indexes[1]], track[indexes[2]]]\n",
    "        radius.append(circle_radius(coords))\n",
    "\n",
    "    # Get the max_velocity for the smallest radius\n",
    "    # That value should multiplied by a constant multiple\n",
    "    v_min_r = min(radius)**0.5\n",
    "    constant_multiple = min_speed / v_min_r\n",
    "    print(f\"Constant multiple for optimal speed: {constant_multiple}\")\n",
    "\n",
    "    if look_ahead_points == 0:\n",
    "        # Get the maximal velocity from radius\n",
    "        max_velocity = [(constant_multiple * i**0.5) for i in radius]\n",
    "        # Get velocity from max_velocity (cap at MAX_SPEED)\n",
    "        velocity = [min(v, max_speed) for v in max_velocity]\n",
    "        return velocity\n",
    "\n",
    "    else:\n",
    "        # Looks at the next n radii of points and takes the minimum\n",
    "        # goal: reduce lookahead until car crashes bc no time to break\n",
    "        LOOK_AHEAD_POINTS = look_ahead_points\n",
    "        radius_lookahead = []\n",
    "        for i in range(len(radius)):\n",
    "            next_n_radius = []\n",
    "            for j in range(LOOK_AHEAD_POINTS+1):\n",
    "                index = circle_indexes(\n",
    "                    mylist=radius, index_car=i, add_index_1=j)[1]\n",
    "                next_n_radius.append(radius[index])\n",
    "            radius_lookahead.append(min(next_n_radius))\n",
    "        max_velocity_lookahead = [(constant_multiple * i**0.5)\n",
    "                                  for i in radius_lookahead]\n",
    "        velocity_lookahead = [min(v, max_speed)\n",
    "                              for v in max_velocity_lookahead]\n",
    "        return velocity_lookahead\n",
    "\n",
    "\n",
    "# For each point in racing track, check if left curve (returns boolean)\n",
    "def is_left_curve(coords):\n",
    "\n",
    "    # Flatten the list and assign to variables (makes code easier to read later)\n",
    "    x1, y1, x2, y2, x3, y3 = [i for sub in coords for i in sub]\n",
    "\n",
    "    return ((x2-x1)*(y3-y1) - (y2-y1)*(x3-x1)) > 0\n",
    "\n",
    "\n",
    "# Calculate the distance between 2 points\n",
    "def dist_2_points(x1, x2, y1, y2):\n",
    "        return abs(abs(x1-x2)**2 + abs(y1-y2)**2)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1: Calculate optimal speed\n",
    "\n",
    "- Change ```LOOK_AHEAD_POINTS``` to influence how many points the algorithm looks ahead (the higher, the sooner the car will start to break)\n",
    "- Change ```MIN_SPEED``` and ```MAX_SPEED``` to fit the track and model !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constant multiple for optimal speed: 1.6854027274097938\n"
     ]
    }
   ],
   "source": [
    "LOOK_AHEAD_POINTS = 5\n",
    "MIN_SPEED = 1.3\n",
    "MAX_SPEED = 4\n",
    "\n",
    "# Calculate optimal speed\n",
    "velocity = optimal_velocity(track=racing_track, \n",
    "    min_speed=MIN_SPEED, max_speed=MAX_SPEED, look_ahead_points=LOOK_AHEAD_POINTS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constant multiple for optimal speed: 1.6854027274097938\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GCsqrZ+gaW7qr+d+fvIU9x8byQRgg5Dd49sgoO1ZXEw6oVrGiLKdU2ubxvafo7Z+gsSbEjvXNnO6fAEAC0bCfoycXZgNMZxyGRuMMj+QaKTPJDNOJFOt7mjFNA9u5MKRkLrHZjKIC8SXN30ZQaBpC0/HV1uH09+UzYRmBIEJ9uZad39LxWzoNsVyGMU0TfPTNa+huCjEylSGRctA1jYBPvfeKcjVmUlmGxmbyXdC9s4E3FgkwMp5Y8FhdE/l88nNqYyHODizcnCaTdXA9Dy/r0Hv2PNMzaUIBHz0dDfh8hprncZFlC8RCCB3YA/RLKd+yXMctFOl5uNks0nFACHSfDzGbyznc3ombzaDpBsLQ8/v/KsuvoyHElq4qtq6qYXgixZe+dwwATcAff3Abu9bWoqtUmIryqiTTNt9+/BhnBqe4fmMzrnNhr/GxqSRdLc2c6r+wvn9sMkltdZixiQsBWpLbsc29KEALIThxephEMgNAIpnhSO8gG9e0YL1MjvtKtZwj6r8LHF7G4xWMlPJCEM4V5HZOmu1e0QwDMxhC9/lUEL7GYmGL//y+rbz+umb+/ekLOzd5Ev7m20eIz6glTYpypRLJLIOjCaaTWc4M5rqUz48naayL5B8zOpkEIVjbWT87AUuQtV3WdTfS0VJDOOSjrbGaSMhPe8vC7IF11eHZ18ksKM9knQX7nCs5yxJFhBBtwL3AZ4DfW45jFpSUC7YevFAsUW2vlRcLWyTHksz9fkN+gzu2NBALmWpjCEW5QtPJLF/9/gFGJlN86E0X8tqfGZripi2trOuq4/iZMTRNMBlPs7GnkQ2rGgEwDQ3D0FnVXkdHSw26rqFrWm5ex/o2ZmYy+PwmlmkgpcQyDbL2hVa2rmtomsDzJLbjMDI2jdAEddURLFOv2C7r5WrO/RXwh0DklR5YEoRAaNqiYFypX5JiEPDpdDSE8Fsa/+Gt63h49wAnBxMc6YuzsaNKLWdSlMvgScnJc5P0j+S6lj1PUh3xMzGd29P8oceO8Cv3bOTGze0IAZapLznBStM0rHlLlHRdQ9c1fNaF36GUktWdDRztHcT1JJoQ9HTUY+gaWdth/+Gz+dZx/9AE2zZ04KvQmdZX/VcLId4CnJdS7hVCvOYSj/so8FGAjo6Oq33Za0rMjgk7qVR+UpZ2ia0GlWuvOuzjz359O9NJm0//f/vzWbaeOzrGp39lE3dubVQXSoryMqSUTCWyHD83wchkMl/+70+e5FfuXsexM2NMxNNsXdNAfSxIwHf1F7ZCCEJBi60b2nFdD13PtZyFEAyOTC7oonZcj9GJaVobq6/6dUvRcowR3wq8VQhxGvhn4HVCiK9d/CAp5QNSyl1Syl319fXL8LLLx/M8PM/DdV28uZnSQmAEAhjBYH5HJKEWqRdUfZWf+Iy9KNXlQ0+eJZ5UG0MoysuJz2T5i6/v4Rs/PcGatgvBbnQyxZe//SKbVzXwS3euZW1H7bIE4TmapmGZBgG/hWUa+UQfcolhYiklUkqytoPtLB4aLGdX3SKWUn4a+DTAbIv4k1LK91/tcVeK53lk0hmc2XEMoQmCoWDuC6NaWEUn4M91k1mGxh1bG1jdEgWkmjmtKJdw9vx0fmLjgVPjvPvudTyxvx/X83jtzg6iIWvF1vgKIWiur2J4dCofkDVNUF8TYXBkisHzU5iGzqqOegJ+E70CGkCV2SE/j/RkPgjP3c6ms/gCPtXVWYQaYwF2rq7mva/r5umDI/xk3wBr26JkbI+w2ktDURZIpB0mZ2wc90IT9NHdZ+lpreLuXe10NUWJhCy0FT7X+SyD7Rs6GBqZygXmhiomplKcPDOSf8wLh/rYtbUT3Sr/QLysf6GU8meltobY87yly9QM+6IUC1v8wbs28b1nzvHtp/s4OZjgh7sH+KP/s1/tzqQo80gp2Xdykjf/6dOgGdTP20b01ECc6oifqrBvxYMw5LqsA36LrrY6Oltr0TSN4dGF6YM9KYkn0itet0Ko+BaxvkR6SsM0UOuUipeU8OSB8wvKTg4mSGcra1xJUS5lPGHz/377OFLCf/6nw3z2gxvpG47jOC43bGikKlz4CahzvY6aEItmTAsBwYBFJuvMzuAu33BVvn/ZZRJCEAgGyKQzSCkxTAPDVCnYipkQuZ2aZlI2t2xqoKMhRN/5BIauPjNFmSOlJJnJXZyeHUnxns/tZUd3jL/44EYaqotrHEfXNTpb65iYSuZTaG5Z18rwaJzB81P4LIM1XY1EQr6y3NmpIgPx3Ow8TdMQmkAXOoFQ7osphFBBuMhVBU1+95fXEwmYPHN4hOdPjLN1VbVK7qEos6ZmbAbHU7zzllb+9ge9QK4naSKRxTKLMz+732ewc3MnqXQWn2UwMj7N6XO5HNaZrMO+g2e5eccq/D4ViEva3H6Z8ekkjusSDQexrNyUehV8S4eua6xri/K5hw6x51guD+6B05OcGkrwe2/foHZlUiqa60ke2X+e//avR/jzD2ziv7xrHY8fHGVtS5j33tFObaTwXdJLEbPd0z4rl41reDS+4H4pJYmZNP5lXF5VLMrv0uISXM9jYGiM+HSSZDLD0PkJ0hm1/rQUOZ7MB+E5zxweUePESsWbnMnyjz89iyfhU/9wkO/uHmJ1c5i33dhMfZWv0NW7LJomCPgXXjD4fSbBgIVtl99vvKJaxNnM4oTj8fgMPl9lrFUrJ5oQWIaGaWhcv64Wz5O8eGpC9WwoFU8TgqD/Qvfz/lNT7D81xX3XNxWwVlfG0HV6OuqZjCfJ2i611WG6Wms5cWYE23Fpb66huipYNvsbV1QgFkuMIQoh1FKlEhTyG/z+OzbQEAvw5IEhhBB89iPXEfKXxw9TUV4tTRN84q2r+dgX9uPONjxuXFtdtF3SL8fvM7l+azfZrINhaDz7wql8Q2pqup8t61qprymP7Q0qKhBbpo5p6gu6NmKxMLquWsOlxm/prGmL8okvPEvWyc2y/MnzA3z+P9yEv0ITxyvKRCLL//NPh6mP+vjq7+xk9/EJNrRH2NgepboIlitdifljxkMjU4t6M88NTVAdDWKUQau4os5Yuq7T1FBNOm3juC7BgE8F4RIlpeTh587lgzBAOuvys/2DvPPO7gLWTFEKZzyR5WcHRgH4/t4hNrRFODGUYEtnVYFrdnWsJdYYV0eDZTMUVVGBGHLBOBQq/SsohXx+6a7GMIah0Ts4rXJOrxDX9ZBIjCUS4iiFk0hd6O1LZlz2npykqyGIu0QGwVISDviIhP1MJ9JEw37WdjcyNZ1i4Pwk9TWR3OqXEg7KZR+IbcfFcVw0TeQ2sC6Dbgwl1211743t3LC+nv7RGbK2y0ffvJaaqL/QVSsb08ksY1MpAGqrAkSCFq7rkUhlef7IALbjsX1dM1URP5b6XRWF1lo/tRGLsekL6V7ffVsrVSW+X7dlGWxb30YylcWyDPa+dCa/Q1Nv3yg3busu6WVNZR2Is7bD8VNDZLK5TR2qIgE6WuvKZqZdpdN1wZe/e4iRyVw+2qDf4DMfvr7AtSoP08ksX/rWC4zmA7Gf3/zl7Qgk3/zxgXz2o97+cd5+1ybqYiFs28VxXVxPYuhaSZ8YS5VA8sB/2MFXf3KG/rEUb7uxmddtrccogyE4yzSwTIMz/WMLtkl0XY/+4Ql6OhoKWLurU7aB2PMkI2PxfBAGmJpOkU5nMdU2PWXh4KmJfBAGSKYdHn6uj/fevVotR7tCMykbT0qCfgNd03jx5Eg+CAOMTaU5MxQHz8kH4TkvHBvitu0d9PaNcWx295yg3+TWHasIBkprglApG41neN/n9pLKuty7q4mephC1EYtImSW4uXjSFoDr5rIlluqYcdkGYik9UunFyTpSGZuICsRlYTqV636LhS2ytkcy4xCfsfE8KIMGwIqwHY/BsQTfffIkMymbmza3cMPGJsYmU4seOx5P01S9uOvf7zOwHS8fhAGSaZuDJwfZvr5N9UCtkOHJDAPjuQvTr/2sD4CuhiCbOqLURUsjkcflaKqPcmZgDM+TVFcF6WypxefLZeMyDaMkU92WbSDWdZ2aWIh4YuEJJaqCcNm4YUMDPS1RJqczBP0m8WSW5togpqGi8OWaSeW6oOfWm37/6V4iQZNdG5p46qWBBY9d3RYjFrYIBy0SydxFkGlobF3TRDK1eAvKeCKD63oYuobjuEiZW8uvAvO14TMXf++DPr3sJjBapsEN27oZHZsmHPJz8PgAtuNiGjpb17cRDftLrmVctoEYckG3pTHGyNg0uq7R2lStTgJlxHUlX/jWARKpXM/Hpu5qfvVNGwpcq9Jydng6H4Tn/OLAIB9440Y+ct8WHt19BoC7r++kJurHbxn88ms3MjAynctw1BQj4DMwZvO1S3nhWM31EQxDI5FMc+bcKI7jEfCbdLU3LNryTrl6tRGLG9dW8+yxCQA0AZ9825qSWz/8SnRdI6hbNNZH2T1v0pbtuLx0rJ/rt3SV3PertGp7hQxDp6E2Sk0sjEBgGGpzh3KRsV2+8+SpfBCG3JjxeDxNLFw+3XDXWnVkcVdzXZUfn6mzpr2alvowACH/hXHGoN9idXvtgueYJtyyvYv9R/pJZ2xaG2P0tNcjPcmpsyP5cb1U2qavf5Su9nq1gmGZmbrgT96zgUN90wyMp7lzcy2NVeW7ikBKyM6bAwS5254svVSJZR2IATRNw1ITd8qO43iMxdPoWu4CKzO72cNYPM2qltJOXnCtpLMO8ZksB0+N0lgdoqMxQnXUx6buWg6eym03Fw6Y3H19V36rvPkB+FIMXaM2FuK2navytw1DJ52xF02umUllKMFzZdF7/tQUv/WlF+huCFIbtfjhviH+7mPbCfjK84JHCEHQb5FM54ZFqiIBamMhjBLsii+7QOy6Hrbj4nkSXRf4rPKaMajkBP0G73ztaqSUpDIOpqHz70/20qOC8Ms6MxTnq987kE+t3t0S5f33bOTtr1nLG2+yyWQdYhH/q95GUgixaMmSrgk0TSwIxsGAD9UxtbwmEln+9vu5fYdPnU9y6nwSgKGJdMnlmL5cPstg6/pWDh4boLOtFtvxGJtIAJM0N8RKqnu6dGp6GVzXY2xyhucPn8N2XEJBixu2dBFSSyjKTjLtsPfIEE+8mJtQFAqY/M47thMp8cQF10oimeWHvzi1YH+TUwNxZtI2jdUhQtdoiYuma3S113Pm3Ciu6+H3mXS01mIYOlJKpOfhSZnfE1wNHS0vWeZdD8GAj20b2zk3OMHp/lyvzuhEgpHxBNs2tGGZpRHiyqrP1nZc9hw8mx+8n0lm2X/k3IK1xEp5SKTtfBCG3DrY7zx5Esct7xPPqyXJLVW6mHuN3y9d0wgH/azvaWbjmlZ6uhrxWSZSSpxslmw6jZPJkE2l8Fy37APHtVIdtvitNy3Msd7dEKS5pvxXiUiZ2wBivumZNK5bOmk9S+Ny4TI5rrdoPGoynlI/7jI0lcig64KAZTCTspHAyGR6UbIJJSfkN7lzRxsP/ex4vqxuNm3ltaZpAk1beKqRUuI6Cy+Q7WwWn9+P6rd+dXb2xPjnT17Pvz0zQHdDkHt2NJZtt/TFdF1b/Nsvoe9RWQViQ9fQdW3BlVBNVbAkF3grl9ZQHeR33rGdeCJLNGTx2L4+mmtDBHxl9ZVeNpom2Lyqjqqwj92HhmisDXLjxpYVCcSXTV0wX5WZtMsXfthLNGiyr3eS5mo/N6+vIVjmvwnT1OnpqOfQiUFi0SAdLTVYpo6Aksm2VVafkGno3LClk+cP9ZHOOlRF/Gxb31oy4wTK5UlnHfYdGcqvcTV0jQ+9eRMtdeGyyKm7HFIZh8npNAd6R2mpD9PZGCUctFjXUcOqlip0TSv4BarQNOS8XYF0wyipVkwxSaRs/vLfjvHzg2P5sp++OMrDf3xL2QdiTQhqq8PcuH0V2azNwRODZLMOAb/J1vVthALFv5yxrD4hXdeojga57boepMy1Akpp5pxyeTJZlx/vOZO/7bge33vqJB9569YC1qp4eFJy7Ow4//TokXzZmrYY73n9BkIBsyiS2miahuXz4dg2nueh6TqGYZRE66UYpbIez/dOLShzPMnIVJbGWPmuJZ5jGjqeJ9l3bCA/RyiVtjlwtJ8dGzsW7YA6H6MAACAASURBVGdcbMqu+aBpuSUUAb+pgnCZyjoutVUB2hsj+fR94/E0colk8JVoJmXz8LOnF5QdPzdJusgmLQpNw7AsLL8fwzQRs+v9Pdsmm5gmNTaKm8ksaDUrSwtYGjtXLVy6Z2iC+qoiGnq4xjzPW7ArE+RSuJZCgg8VqZSS4zN13nB9J4mUzX239vD48334LQPLKnxLrxhIKZecMbrUrjWFdnEL2LNtpk71kp2anHsANRs2YobCBahd6QgHTD719rUMTWZ46UycqqDBn753I5FA5ZziNU3DNHVsOxeMg34Lv99EK4FelrL4lKSUZLIO6ayDqec+DDUuXJ5mUlm+8eMjDI4lgNz48PvftJnqiA+f+syB3JrqO3e0850nT+bLSmUim2fbF4IwgJRMnz1LbPUaNFOtEb+Uxpifv/rIFmxHIgQETK3sx4fnM02dbevb6D07Qk9HfW7DEUMv+FyIy3HVn5IQwg/8HPDNHu+bUso/utrjXolU2uap53vz64Vb6qvYtKZZdU2XobGpVD4IQ258+KkX+njbnWsLWKviomsa29c2UFcVYO/RYVrrw+xc10i4mGZIvwzPdReXOQ6S4mvNF5vJRJYHvn+SR54fAqCjPshffWwndVXFP1lpOWhCEAn52bSmhb6B0XyvkGnotLXUFXVu8+UYI84Ar5NSbgO2A28UQty0DMe9LI7rcuTU8IKkHQMjU6Qzi/ciVkqfEILbt7ezc10Tvtmu6HTWLYlxoJUU8pus66zhXXet447tbcW1TOkSdJ8PYSy8gA42NKAZqjX8SvrHUvkgDHB2JMm//PzMkolcyll8OrlgaMZ2XGaS6QLW6JVddSCWOXNNFHP2vxU7K7quXHIv1LlE4Er5SGVskuksY5MzmDq8755NNNWGuGlzCwFfZZ+oM1mHqUSGyUSGZPrCRaihl9aOY5ppUrtxM/7aOsxwhGj3Kvw1tSX1NxTKqeHEorLjAwky9uJehnLmOIv/3qXKismy9N0KIXRgL7Aa+Dsp5bPLcdzLYZk6rY0xJqdT+TJNCGKR8k/tVkk8T3L87DiP7T6VLzs9OMk77t5EoMKHIGZSNj/f38cTL/TjepJNq2q5/841hEswx7oQAt3nI9LZBVIidF0F4cu0Y1U1QizMi3L3jkZC/sr5fQghqKoKEU+kEAJCQT+6rhGJBAtdtUtaluVLUkpXSrkdaANuEEJsvvgxQoiPCiH2CCH2jIyMLMfLzh2X1sYq1nU3EPCbxCIBbt7RrSZrlZl01mb/saEFZTMpm3Taxl9BE1KWMjaV4mfPn8OdnRV9sHeMF06MlHR3vabraBetK87G48RP9TLd10d2erqAtStO1RGLv/i1bbTVBagKmXzo7i5u31RfcRcypmHQ1lJHZ1sDtbEQsbAfXRNFnep4Wc9gUspJIcTPgDcCBy667wHgAYBdu3Yt6ztimQY97XW0N1WjCVH0i7eVV0HCG2/uwfMkg6MJfvHiObKOi2kW7wSMldI7OLWo7HjfBNevb8rvK1zqMlOT7P/c/yAzkUvuH+7sZPNHP44ViRS4ZsUj6DO4aX0ta1uvw3E9fIaGZZRdqohXpOsafmGQTafzwddzXUyfL5e9rQgtx6zpesCeDcIB4G7gL6+6ZldI0zT8vsr70lWCdMZm3+EBTvTl0ve1N1XxljvWsvtQP8HL3Li+nPW0xhaVre+swSyTk7DneQw88UQ+CAMkzpwh3nuSum3bC1iz4pNIO/zshUH+9fHT2I7HXTuaef/dPVSFSm+Y4mpIKRe1gB3bzm23qRXf72I5atQM/FQI8SKwG3hUSvm9ZTiuogAwMpHMB2GAvqHcrPh7b12rAjFQG/Vzzw1dmIaGJmDnugY2r6ormy5J6bqkzp9fVJ4aHS1AbYrb0HiKf3j0JOmsi+tJHtk7wO6jo0XdLbuiivQ3cdUtYinli8COZajLq+J6HrbtIgFjNrOKUl48z2PLmkbODk4ylcgAMDQ6zeqO2gLXrDgE/Sa3bWtl14ZGJLnMY/4yGp7RTZPm225jdP/zFwqFoHaLyi1+sRd7xxeVPXtkhNu3NOKroHOjECK3qYiU6JoGQiyac1BMSvrXajsuA+enOHxyCMf1aKqLsGVtq0rkUSZc1yOZzjI6MY3jety0tYP+83EOnBimszlWEqnrVopl6mUzHryUcFsb6z/0q/T95MfopkXXfW/FVxUtdLWKzoaOxcMU21bVYFbYrmRC0zB9PqTrkBkbw7NtzFAIURVD04vvd1LSESuTdXjp2ED+9tDoNNHwGKs76tGKcBxAuTIZ2+Fnu0/kcyQPjU5z49ZOLEOjsVZN0qkkZjBE/c7riK1bjwDMsMo9vZS2+iBvvbmd7z17Ds+T7FpXx+1bGksizeOy8zySA/3I2WxtmcksnvTwV9cW3ThxSQfiyXhqUdnIeIKu1lqsInujlSs3PpUkFLCYnsnky84NT7J1bWtZt/5eiScliWSWE+cm0TTBqpYYkaBZtN1uy0UIgaUC8CVFgxbvee0q3nZrB1LmhikiwcqcRyFdNx+E5zjTCWRVtQrEy6kqsnifzdpYSG0OX+I8T2I7LromWN/dgN9nsvfQOZKpLD7TwNDLO+C8kumZLH/1r3tJpnNpXSNBi9955w6iocrIKTxfZnKSyeMnGD90mKabbiTU3IwVrezekqDfwJMewxMpDp6aYG17Fa11oZJJc7pclgq2wjCgCE8fJR2IfZbB+u5Gjp05j+dJamMhutpqVbd0icvaDs8fOpvPF+v3mVy3sY1fvHCanva6iv98nzs0mA/CANPJLC+eGOG2bW0FrNXKy8bj7P/rv+XMDx4G4KUvfpnrPvUHdN93L1qRrhddCVnb5afPD/DNx3vzZa/f1cb9d6yqqN2YhKZhRqN4mSx6IIjQNXTLh6YX33tQfDW6ApZp0NVWQ1tTLDc7TtdURq0S53keQyNTyHl756YzNrbtctdNa7Eq+AQLufWRM+nFG5rMD8yVwkml8kF4zktfeoCWO24jUFu5M+qTGYfvPH16QdlP9vbz5ps6KisQ6zpWNEZmcoKhZ57GSSWJtHdSu3Ubhn9xb2ohlXzTwtB1/D6TgN9SQbjEua6H63rUVAXZtqGd9uaa/H2e5+G3zMqcdDKPEIKbN7cw/23QNcF16xsLV6kCke7iXYXcTGaJR1YWKXOb4cznSUklLiX2HIeBx3+KPR1HOg7xUyeZPHp4ye02C6nkA7FSHjzPI5lK0zcwyuh4nOGRCaIhH421UTRNUBMLFbqKRSMW8fHb79zJ1p46tq+p53fftZNohWVOAjCCAeq2b1tQtuad76j4GdV+S+eOrc0LynauqauodcRz7Ok40lt4wZboP4dnF9fufKoJqRQFz5NMTScXlE3GZ2htitHaXI1ZxJt6rzSfadBSF+Zdd61DAlaFvje+WIxb/uy/cubhRxh98UXaXvc6mm64HsNXeZPW5gv4DN5+5ypWt1Wx79goG7uquWF9A+FA5c2eNoKLL+CtqhiiyMaJRSFSn+3atUvu2bPnqo+TyTqMTc4wPjlDU32UaNivuqdLjJQSpMTzPFzPAwTDI5PYs/uHtrfWYVb4uLByadLzcG274gPwUrKzqw8cV86mQK2soR03m2Xi6GHcTJZgQ2N+ApcvuvLJYIQQe6WUu5a6r2TPcFk7l8xjaDQOwOmBcdZ1N7CqrQ5dLV8qHVJip9MXbgtBY32Mc4Nj+H1mxZ04lCsnNE0F4ZeRzbo8f/w8R89OsqGrhm2r60pyn+pXS7csop3dnH3kRxz44heRnkfLHXey+h3vKKqdu0o2EDuulw/Cc06cHaW9qVoF4hLheR7S8xBi3l6hUiKQVMciREJ+9CJMR1coqYyN60r8PkOtlb8E6XmkJyZIj45ihiOYkXBBWkCFlkzbfONnx3npZG5zjEOnxzg9OMX9d64hUEGzp2cGBjj1ne/kb/f/9DFqNqyn6aabC1irhSrn01CKxlx3tHSc3LIz00RKiWvnluUIoCoSqPj1wnNc12M8nuLR53qZSmRY31XHjZta1c5TL2NmYICf/MbHyUxMAtBz/9vY/LHfwFdVVeCarays4+WD8Jx9x87zlltWVVQgHn3pxUVlI/v20XD9DUWTd7pkz3SGrtFYt7BroaetTk3qKQVS4qTTeI6DdF3cbBZmd0sB0A1DBeF5UhmHf/rRAfrPT5NIZtlzaIDnDvbjOIuX71S6bCLB/s//bT4IA5z8t28vuF0pBLmlbfNVYk9KzYaNi8pqt2wtmiAMJdwitkyDrWtbGa1PMDoxQ3NDlFg4oLqli5jneWRtFyklQtPRpcfc4kbpOLltyma3LFMuiM9kyNoL1z0ePTPGro0thI3KGe+7HF42S6Lv3KLy1PkRol2dBahR4fgtndfsbOcne87my16/q6OiWsMAkc5Oeu5/O4HGRqxIBCMQwFdT88pPXEEl/Yn4LIPWxhitjYu3/lKKi+N6jE0mOHh8ENtxiUUCbFvXii5nM0LNtohVS3ixpbqgq8I+jApPbrIUKxql4w13c+CB/5Uv030+ot2VFYQhd358zfY2NnfX0jswxerWGDVV/orbMMWKRGi86Sae+I+fJH76NJppsuW3Pk73ffcWzSYi6qynrAjP8zh2aji/LGlyOsXR08N4s4FXM00VhF+G39K5fkNL/rbP0nn9Davw+9QY8cU0w2DVL7+NDR/6IIH6emo3b+K1X/4CVqwyL9ZDAZPOpiiv3dlOe2OEQAXu1W4nk7z0hS8RP30aAM+2eeHzf0N2Kn7pJ66gyvtUlBU1k8py/Ow4I5MzrO2oJ5u16e0bAWAinkKiYfgt1R19CX6fyU1bWtm+vol0xiEcsNRErUvwV8fY+OFfZfW73o6mG/hilTVJaymZrMPkdJp9R4eoCvvYurqRcIXsxuSm0owfPrqofGZggHBryxLPWHklH4gz2dzMWyEEvgq82itmM6ksDz12mNHJXMasl06c556beqipCjI+lSQWCWAYetHtDVqM/D4z1wIujp60oqdbVkVv/HCxofEZ/vmRg/nb+48N88F7t1bEmmIzHKL55hs53tcHQmD4/bjZLJGOjkJXLa+kI9dMKsO+Q31MTaeJhv3s3NhOKGCV/QbpxS6ZtsnYLlnb5aYtbTz9Qh/j8RQAew4PcOeODhzXY/2qJgw1y11ZIZ7r4mWzgEQYJrpZGb0KqYzD0y/0LSibTmYZnUhWRCDWfT42fOiDRHt6iK3uwU4kCLe2YoaLJ399yQbiTNZh90tnSSRzu63EE2mee+kMt+7oxmdVxg+sGM2kbH747GmeeKEfgPpYgA+9cQPf+fkRMtnc+HBtLERLQ1SlI1VWjJvNMn36FKMvvoDnOERX9VBXhNvhXQtCgFhiYl8lNVj0YADpujz2Gx9Heh6638+df/NX1G7eVBTvQ8n2CXqelw/Cc5KpLK5XgXt9FQHX9ZhMZEhmZpN06Lkv98hkiideGGB9Zx0At2xtJxxUW1ZeLtf18Dy1XvhqOTMznN+7B8+2QUriJ0+Q6OujELn2V5rfMrh9e8eCaRjVET91sUDhKrXC7ESC/f/z8/mdmNx0muf+9DNkJiYKXLOckj0bCiHw+0zSmQubpFumrnITF8BM2mbP0RG+9uOTpLMOd+1o5YNv3MhXv58bkxocn+GGDQ1sXt1ALOwviivQYmfbLtPJDId7hzENnY09jQT8JroaT39VkueHF5Ul+s8R6eqqiC7q+liQD791Owd7R6gK+elpryZUAd3Sc9x0JncRNs9Mfz+ySBpuJRuIfZbBdRvbee7AGWzbxTR0rtvUoVpaK8zzJKm0w4OP9TI1k9vj8wfP9dFYE2B1a4wT/ZNsX1NPd0tMJVu5AtPJDD948kj+dm//OPfdubGiTp7LyV9bt6gsUF9fVNmVriXL1KmtCnLHjspbTw25vauDjY0kh4cJNjehmybR7m50f3FsFlKyUUsIQVXEz527VuN6HrqmYZo6mkpysCJcTzIWz/BvT/UxlbT52H0b2XtshEf25LIavXByjM2dUVrrQ9y4oUkF4SvguB4HTw4vKus/P8XazvoC1aq0mZEIsXXrmTx2FKQk0NhEVc/qip2xn7UdPE/is4yK6KHy19Twmi/+LemxUVLnR5CuS922bZjBYKGrBpRwIAbQNA2/rzJ/SIU2kcjy4f/5LNOpXGasH+0Z5C8/vJ0XTo4xPJFiTWsVr9nRimXqFbtx/aslBJjm4u+1aajv+qtl+HzUbt5C9foNICWaYaBX4NaJrusRn8mw7/A50lmHdZ31tDfFyn7ppxACw+9jz59/lnjvKQB81TFe/7//nmBjY4FrV8KTtZTCyNguo/EM00mbT759A92NuSUAnoTvPtPP9evqWd0a5a6dLYQDlgrCr4KuaWxa1bigFyHoN2mqrbyt/JaTblmYwSBmKFSRQRggnXV4+KkjDI5OMxFP8cxLZ+k/P1URk9ZGnn8hH4QBMhOTHPuXb+A5TgFrlVPel0HKskplXX5xeJT//s3DpDIuHfVBPvWujfzp1w8wPJnGMjTuvbGdt93aSTSkxjKvRtBv8dY7N9I3NIll6jTXRQmobFrXxPwgVO7dtGOTM4tWlhw/O0prQ1XZt4pTIyOLypJDw0jXBaOwf/tVt4iFEO1CiJ8KIQ4LIQ4KIX53OSp2ubK2w8RUklPnRokn0tgX7VKjLJ9UxuErPzhBKpN7j8+OJPnqI7380s2tWIbGB+7qprbKr4LwMtB1jVDAYn13A6vaalUQvkak5+HZWdxMGs/OImV5LxVb6nsU9JsVMbem5Y7b0QwDIxCg8YZdVG9Yz5p3v7MoekeW4zLAAX5fSrlPCBEB9gohHpVSHlqGY1+S7bgcO32e0/3j+bIta1tob4qpDQSWke24TCZs9vdO8vG3rEEXgs9+8xDxpMPRc3F+4009vHZbIzURFYCV0iGlh5vN5NeWSs/LrYG3fGXbMo4EfTTVRRganQbAMnS2r2upiH3c/TU1vOHr/4CTSjH09C8ItTQTbimTXNNSykFgcPbf00KIw0ArcM0DseN4C4IwwJHeYRprI2oS1zLqG0ny8b/ZQ3Z2I/ptq2L8/v0b+KOvvcT2nmra6oKE/OXdraWUIUk+COeLXDe3R3aZBmK/z+S27V2zaWgdqsIB/BWyP7Hh9+FmMjz2kY/lx4Wj3d285u8+j7/A+xMva7QSQnQBO4Bnl/O4L2epCQauW95dSyttJmXz8N5BwoELP9YXeiexTI1bN9bxO7+0VgVhRSkhfp9JTVWQ5rporlu6TC86LpZNzPDSF7+8YHJW/NQp4qdOF65Ss5YtEAshwsBDwH+UUi7a6FEI8VEhxB4hxJ6RJQbNXw3d0KipWrgOrK05hqHWrC6L6aTN4ESaWMjiD9+5gU/88jr02bEkXRN86l0bqK8q/1y9K0VKSTbrkEpnyWRtdVF5rQmBZiwcM9WsytmS07YdZpIZpmfS2HbhZw5fc56Hm8ksKnbS6QJUZqFlacoIIUxyQfjrUsp/W+oxUsoHgAcAdu3atSxz5X2mwXWb2jkzMMFEPElTXYSmuiq1o88yyNguD+8d5O++ezxf9u47OnjH7e384LkBeprDRCtkP9OVks7YvHi0n2zWQQhY1V5PQ10Eo0KyP600IQSaaSIMA+l5+Xkl5To+PJ9tOxztHWImlcuG57MMNq5pKevMhFY0woYPvp+Rfc8T7e6met1aMlNTVK9bW+iqXX0gFrlv7d8Dh6WUn7v6Kl0Zn2WyuqMe1/MwdK0ifkQrYTrl8H8ePbWg7KGn+vji/3U9v3RTK7GwCsLLyXZcTpw+Tzaba5lICSfPjlAbC6lAfA0JIXLnjAqb3BlPpPNBGHK72Z0fjdPaVF3W59CazZt40zceZPLESYafeY7ON96DKILf13Jc/twKfAB4SQixf7bsP0kpf7AMx74smibQtMK/meXCdj08T/InH9hCwKfz6L4hvvX0ORxXEg0aNFZXzq4tK0V6csGJcY7tuPh8aumSsrzmb5YzJ5WxkVKWdSDWTYuzj/6Egw/8LwB6//07tL7mTnZ9+lP4qgqXMGc5Zk0/CZTvJ1eBegcS/N5X9jGTdtE1wW/eu5q33tTK8ESKgE9d8FwLmi6orgpyfmz6QpkmMMu4q7BYeZ6H7XhMxWcwTYNwyF92y3tqYiHODS3cArCxNlr2yz6z09Mc/cevLyjr/9njbP+Pv13agbhYuK6H47pICbouMAucKaVUjU9n+My/HGQmnUva4XqSB354kq/87g1EQ6YaF75GDF2nu70O1/UYm5wh4DdZ292IofJLr7h0xuFo7wBzizL8PpM1XU2YZvkEY8s02LC6mb6BcTwpaWmIEayUnb2WaDaKArclyyJa2bbL4MgkvX2jeJ6kNhZiw+rmsp54cK0I4I5N9WhbNZ546TynhmfIOh66JqhW48LXlGUarO1uxPMkCNT3twBc12Xg/ATzV0amMzbpTBbTLJ8hGV3XiIYDrF3VBBIMozLm11iRCOve/z4O/f1Xab7lJkLNzWg+H3qgsJ9tWVxuZ22HE2dGcicwcvlU+4cm8Ty1/ONKpLMuI/EMvcMzHOmL85E39fDO29upi/oI+sunNVDMDEPHsgwVhAtEQv48Mt/F+ZnLhZSQdVwm4klSmfJfMqf7LFa/437e/I0Hqdm0idToGLUbcztyFVJZ/NrjidSisvGpGdqaqyttMuRVGYtn+M2/2ZM/6ew+Nsb//OhO3nZzGzGVP1qpAIau01gXJTFzYW3pXN7vcmPbDr3nxjh66jyQ+ztv29FNLFoce/ReK9L1+MV/+RPGDx4E4NxjP2XTRz/C+ve/F90qzOdcFmEqGl7crVBTFUJXUfiKPPr80IIrfynhkX2DNNX4KyIpfKFIKfFm8xwrhRcK+lnb3UQsGqS+NsKGnpayzE3guF4+CENuns3+I/1ksuWd3MNJJvNBeM6xB/+F7PT0yzzj2iuLFrFlGazurF8wRtzaFFPB4wpt647xF7+2lbTt8YPdgzx3dIzaqK9iUuAVgud5ZLM2dtZGN3T8fl/Zz1wtdoauEQ75ZycvibI9j9jO4m7oZDpb9heEYonMi4VqCc8pi0BsGjqtjdU01kVnZ01rZbfc4FqbTmY52jfBj3afI+g3ePvt3WzqiPLmG1oqYhJHIXieJJ3KkMnk1g87jotjO4QjIRWMi0C5fwaWqeOzjAUt4JaGqrKfqW8EArS99jWc37uP9rtfhxmJULtpE75YrGB1Kpt3XNc1fJaJ32eqIHyFpJTsPTbKvz1xmpm0w8hkmi9/9zB3bW+kLlr4vTrLl8wH4Tmuq7qoi1XWdphJZZmeySyZEKPU+CyD23auor4mTMBn0t1Wy4ZVTWWfyc1XVcV1//cfcNffP4BmmSQHBzBDAdzU4rlGK6UsWsTK1UllXZ46OLygTAIHT0/QVh8qTKUqhBBiUeAt9JpGZbFM1uHAiSFOnB0FIBLy8drrewj4S3cSlxCCcNDHrk3tOG5uiaLPqoyQIB2XJz7xCexEAoDh557jxj/+Y5puurEg9SnLd91xXLzZk5th6GqM8xVYhsaN6+u5ZWMjui549vB5dh8dpbMxXOiqlTUhBMGgn5mZC1filmVWzO4/pSSZtvNBGGB6JsOh3vNsX9eCXsK7vWWyDiOTSX7xYh9CCG7Z2kZdLIRVRslLljJx/Fg+CM858dBD1GzaiBWJrHh9yi4QZ22HU30jTEwlMY1ctqKqSLCkfyzXmu141ER8fPPxXhzX47U7WrlrZystteW9jKHQhBAYpkG0KoxtO7mLRk0r28lBpSw+s3irvIl4MteSLOFzSzyZ4V8fvTCDuG94ig/eu43aqvL+7ZuhxT19ZihUsA0gyioQe55H//AEE1NJIJcw/9ipYXZs6ijpH8u1NhZP8/mHXsrf/ufHTvAHv7KdqFo7fM3NTQjSy3xcrtTVVgUR5IZs5rQ3xkp+PsqLxy8akpJw4OR57tzZVZgKrZBwWztVPT14tk3rnXcgdJ2W22/HDBbmAqSsopPjekzFFw+4p9KlP7HiWtpzZGRR2RMvDuKUeZYdRblcuYlN3YQCFoausaazjs7WmpLvvYgGF0/GXKqs3PirY9z8mf/GdZ/6Q9x0Cmcmgec4uJlMQepTVi1iXdMIB32LZjT61TZyl9TaEKKxJkBnY4TzEylOD03TXh8q+ZNMsZJSIh0H6bmgaQhdV9t4FjnT0Gmuj3LXbJetaWhlMbt4w6p69h8fYnomN3s/GvKxtrO2wLVaGW4mw8GvfDmf3nLy+DG2f+L3CDY2rXhdyisQ6xrtLbUk01mSqSxCQEdLbdmvi7taa1qqeO/rVnP4zDhbu2uorfLTUhdSk9yuETeTIX7yOJ7jgBCE2zuwolVoZXBiL2dCCAJldlEfDli8954tjEwkQUB9LFiW6TyXMvzcswtzTEvJ0LPPsuqtv7TidSmrQAy5LqQNPc24nkQTAl3X1PjwJdiOyzOHhvjOk735sp1r63nP69cVsFbly7NtEn1nckEYQEoSfWep3rARVCAuScm0jet5aJogVGLLmTK2w+hUmqcODuK5khs3NdPeoBHwlV1oWMRXVbVEWWGSepRlhDJNA7/PxLIMFYRfQTLt8KNnzywo23dshEzWLVCNyp9zceIAKZFqPL4kTcRTfPMnh/jKt/bxzR8fYmwqWVIJWeKJLH/9zefZe+Q8zx8f4UvffpHRycIltlhJddt3YM3LpmVVVVG/Y0dB6lL+lz3KKyqlE0fJ0wRmOII9/f+zd+dhklX14f/f5y61V3X1vvdMz74ww8A0m+w7CLiRKLihoOjXRGOM+cXtG03ik5hE4xKN0a+ACoqJMSACsoMiyDLsszNrL9Nr9VL7cu89vz+qp6ZrumEGurt6qfN6nnmgT9WtOrV+6p7zOZ8TLTQJXVfD0gtQIpXl17/bxfB4gmhkLMWdj+3kmktOWDDDu8/tHpi0A+ATWo5dmAAAIABJREFUr/Tw7tpVi7/EZyjExk/+BXYqhTAMNENHd81NotqiD8SWZZOzbKSUmIaBucgXqr9RXrfB289ehmno1Fd66RlK0DMYx62ep1mh6QaBllbi3Z3kYjF0t4dA25I5W7+ovHm2IwtB+LCxeGZBrTaoDE4OPJUhT9nUl9d0jUPPPkWytxeEILx6DXWbT8HweEraj0UdiHOWzYGuAZKpfEagyzRYsbQeU226XmAaGuuWVnP7QzvoHoizrKmC91y4Gr93cSWlzCe6y0WwbWkhUUQz1XO9EOmaIOR3E00cWfLi85gYC2g6bO2SamrDXgbHh6Mr/C5OX9dYFoFYOg6jr76aD8IAUjK6cwfh5SsxGkqbOb2oI1IimSkEYchX3YqMxKmvrSiLN9rxiKVy3PSbVxiO5SsH7Ts0xm337+CGq04gsECG1xYizVjUH72y4POYXHn2Ku58bCfJdA6P2+Bt56zGs4ASndymxsffsZH+4SQSaKr2UxFY/OuIARzbJtnXO6k9OdiPTwXimZPJTi7kkc7kkFKqQDzOsuxCED6sayCGZat545lkpdNkx8YYeuklfI0NhJYsxRUKzXW3lGkQQlBX6ecDb91IznIwDA2vy0BfIHOrtu3wyv5hvvO/W6kKetA1wWWntXLOhkbcrsU/VaIZBsEl7cS7OovaA80tJe/Log7EFUEffQOjRW3VlYFFn4TwRhh6fqlCKnNkT9LKoBtdFfOYUdH9+3jpm98sDEdXrFrFCR//P3NSYF6ZOZomFkxi1tFiqRy3/HYXUubL3ALc/vAeOlbVlkUgFkIQXNJGOrKe0V07EIZBXccpmP7Sb3azqAOxaegsW1JHb/8ojpTUVYfwLtAPzWzxeUw+dPl6RuNpqiq8OI4k4DHVHPEMysai7P2f/ykqHjC2eze5WEwF4kUok7MZjaV5dkcfFQE3J66oJeSff8O9UkpiyeJRw5zlLKhks+kyPF7qTjmVmpNOAkcixivdlbwfJb/HEtJ1jaDfi7fNhSR/9qeGpIsZukZN2MvDWw7QMxjDbepcddYKwkF32exNOtukZMoatk5O1UBfjAaGE3z/jhcLv7ueeKmHP/uTkwj65tdJgMvQ2bi8mpf2RgptS+oDZbdiQjo2Qy++QHZsDISgYvlKgkuWoJcwibIsxmgNQ8c0dBWEp5DJWjz4zH56BmP5v3M2v3psF2lV0GPGuAIB2i65tKjNU1NTVExAWRzSGYuHthwsWps7lsgUPl/zzYcuW80FJzfRUOXjrA0NfOZPN5bVrmuObRPdtzcfhAGkZGzP7pJv/lB2pzyO42A7+U+JOkOGrOXQ2R8tapMSRuPpssmenG1C06jdvBlXOEzvHx7H39hE8/nnT1liT1FKIWc5PPxiHz99cC8XntTIRR2tBL0mnjIbBZO2TWZkdFJ7LhbDFSjdXHFZPeuWZRMZjRMZjqFpgvraMKGAt6zLYLpMjSUNIV7ec2QrRE1AOFDaBe2Lnen3U7NxI5WrV+er+KgCHouSx21wUccSXu0aKZwVV/jdNNfOr1yAWDLHTx/aSyprc/fT3UA+8eyWv3oLPk/5hAXNMPDW1pKNjhW1uypKu6JhRp5xIcTNwJXAgJTyhJm4zdmQSKYZGMo/4bYD3b0RVi5tQNfLZyjmaG7T4OJT28lkbRqq/dRV+qkMusui6PtsszMZMmOj9D/zDO5wmJqNG3GF1FnwYldX5ecv3r2ZZ7b3EQ64OHFl3bybH5ZANleclOU4EqfMyt0KTSPYtoRcIkGyvw/NMKlcuxbNLO3rNVPftj8Gvgv8dIZub8Y5jsNoNDmpPZpI4VlgO6bMtJDfzRVnLuex5w+ypytCW0MFZ21qw1VmSRszLdnXx/Nf/xdw8l94XQ88wEmf/Wu1fniRc5s69VV+rjpreVF7NJFlYCSJIyX1VT4q5jCTWtfggk0NPPj8kYIWm5ZX4imDZUtH091uqk84Ib8DmsiXoS31iNWMBGIp5e+FEEtn4rZmixACr8dFNF5cG9brLu8gDPni9Xc8touh0fwPla17B4kns1x51qoFVSVoPrFSKQ7c85tCEAZIR4aId3dTtW7dHPZMmQtjiQzf+MWL9A3nP2PVIQ9/876TCc9BHsZIPMt/3rOXCzfV01DlY/vBEU5YWsklm5sIzbMz99IRWKkkmeEIutuLt64WvYRnxSWbHBVC3CiE2CKE2DI4OHjsA2b+/qkMB/BOOPsNBb1Ff5cry3YKQfiwA71j5GyVOT0dU21tKB31nJajl/dGCkEY8gU0ntw6ubxiKezvS3Dn0738xQ9f5OlXR2moCVIb9hL0luePbuk4pEeGiR3YTzYaJTXYz+irr5Z0eWHJnnkp5Q+BHwJ0dHTMyUSEaegsbanFdhwEAk0XGCppBl3TMHStaCG/32uWfUb5dBheL0ve+lZGdu0sFPJwVVQQbG2b454pc2FoLD2pbXA0heNItBJXsdvelV8l4Uh4ckeEJ3dEOHt9DaevqcFbhl+Hjm2TGhwobstmcCyrZBuylF26sGHouF0mLpehgvA4t0vnglOWFv7WhODS05fjc6vqWtPhb25h8+e+QMNbzmTJFVdy8v/3OVxqyVJZOn1dPUeH23M3NaNpAillyfYEH4pm2LRs8vr1izbV4XWX5/ehAIQ2xWMv4YmImKk3wPgc8d3HkzXd0dEht2zZMiP3OxMs20bK8l5XnM1ZZHMO1vhwtKFruExDJWy9CblkEjudRmgC3eNFd7lAiLJ9bymQzlp09cf59R/2Y0vJFWcsob0xRDxlcf+zXQBcekorVSEX5iydIAxGM1zzjef5kzMaqPDq/PThA6SyNn96VgvvP28J4UD5TtNlo1HG9u0p/G0GgoSWLJ3RM2IhxHNSyo4pL5uJQCyEuB04D6gB+oEvSylveq3rz5dA7DgO6UyO3oFRHMehujJIKOgt2zPlWCLDbx7fSSyRQROCU09oYU17LW61f/NxyyUS7LvzDjLD+bKB/pZWllx6GYbPN8c9U+aDRCqHBAJek4GRFJ/+j6fIWvkpIZeh8a0/O526sHdW7vvJncN88DsvAvDWk2t552kNVAZctNf7qPCV9+iXY9s4Vo5sNIrh8WB4vDM+LP16gXhGhqallNdKKRullKaUsuX1gvB8YlkOew/2k0xlSGdy9PQNk0iWtrTZfJHJWjz58kFi45ucO1Ly1CtdZLLWMY5UDpNSMrJjeyEIAyS6u0hMseepUp78XpPA+IYqDz3fUwjCkK9y99DzPTN+n4m0xZ7eOKPJI5/le58f5KPff4Wv/3rvpCHzcqTpOobbg7e6BsPnL/nGD2U3RzxRLJma1DY8Gscuo91HDrMdh8jo5HXWiWR2DnqzMEnHITXFioD00NAc9EaZ76bat7ih0kckmmHPoRgDo2niqeln7u4+lODyrz5DTdBFQ7h4udSfv7WdUJmfDR/m2DbZ6BiZoUGyY6M4JVw1UtZjjq4phlxdplHKOfp5wzR12hrCbNt3JHtQ0wQhVeryuGm6TuW6dYztebWovWL58tc4QilnF57cxN1PdZIa32BlZXOI1rog13/jjyQzNkLAhy9ZxtvOaMHveePBciiaZSSe5bu/PYCU8Pf/vZvvfvQEHnxpiOF4lvef08KSutkZBl9opG2THRnGyeZPPOxUCmnZuKuqSnJ2XNaB2ON24fO6Sabyw7GGrlFbHUKb4pfqYmfqOievbSaTtdjXM0LA5+Lcze1qfvgN8tU30HTueQw+/xyaYdBwxlswAvOrzrAyP1QGXHzzE6fz+5fzUxdnbWjg7257hWQmH5ilhP/+fScXnNRIdHxY2evWCb/O7khSSiLxHJbt8LHvv8zZ66ox9fyZxc6eOO/95gucd0I1f375Uta1qvflYVLKQhA+zMllkVKWZOi+rL9lTUNnSXMNOcvGcRxcLhOjjDeA8HlMzj55KWec2Db+5hNYto2uq4zf1yMdBzuTJtbZCVJSsXIVFcuWg6ZheL3quVOmpOsaNRUe3nV2OwDD0QyHIsXTZV+49gS+9std/GF7fnrjwo21fOadq8jZAJKARydnQzpnY2ga27tj3P54D1d21LOtK04sZfMP713NY1sjWI4kazls74pRW1G+GdJTEiL/b2Ly8uG2EijrQAz5dcWGUZ5Z0lNxmQaOk2Prnj4OHhrB6zHpWNdCVYUfwyjfHymvx86k6X7sUaSVP2sZ27eX5vPOx1SZ0sob4PXonLm+lvu35M+Q17aFODiQLARhgKtOb+ZLt+/ikVci1FW4+NEnTuSzP9nOwFiG7924gRu//zKbloYYiubP7jqHUtzxdB8/+8uTeGxrhOZqDxduqKE2pLY4nUhoGq6KMNnRkUKbq6KiZD+i1TfrFGzHIWdZZZm05TgOr3YOsbcrgmU7xBIZHtuyl2xOZU+/llhXVyEIQ36+KXrgwNx1SFmQvC6DGy5dwVtPbSLsNzlldQ17exOFy9e1hegcSvHIK/ms/GvOauY79+xn96EEG9pCPLEjH0S2d8fYvLwCt5n/er/z6T5u+N5LXHpSLdec1UxthQrCRxNCoHs8eOrqcVdV46mrR/d4ESWapiz7M+Kj5SyL/sExEskMPq+LhtowZhnNk2ZzNj39xXtzSglj8TQ+rxrOOm7j1ZLUsLTyRlQGXfyfK1dx3UXLcJkau3pi/M+T+SVNzdVedvbEC9dtr/Pxiz/kL+sfy3BlbT7xKmtJ/vOBg9z8ZydyyyNdRFMWN1zYSmuNSsx6PULTEJqGHE/OKuVnV50RT2BZNl2HIoyMJcjmLEajSQ72DGFZ5VOoX9c1KqbIlPaX7a4sxxZsbUXoR36sCV0n1N6ugrDypnhcOlUhNwGvyYrGAJ+8ajkBj0HnQJKLNtYWrrfrUJxTVuTLVe4+lKA6aHL6qkoAHnppiO/ee4C/v3Y13//YBi7cWFv2RTuORUqJdBycbBY7k8Gx7ZKVHi2fU73jIKWcVNAjlc6W1WbZpqGzcXUTkbEkiVR+nmlNe53Knp6Cncthp/LJNc3nnU+s8yBISXDJEnS3WvalTF+F38W157RxRUcjknwd+C9cvYLv3nuAu7f0cdOfbSISy/HU7hH+6Vd7+N6NG9AEWI6kKuCiJqR+QB83KbFSKSD/fW/bFrrbgzBm/7tvxmpNvxHzpcTl0XI5i1f392FP2ENW0wSr2hvLangaIJ3JkbPs/M5Mhq5qTh/FzuUY27MbO5P/4SZcLipXrkYv0W4tSvnKWQ6jyXyhj5DXJJW1SedsdCGoCpjoZbzyYzocy8LOFO+SJTQd3eOZkdGt1ytxWV7R5Rh0Xae5oZLOQ0dKFDbVVSKkg3Scsirc73GbeMZ3X3IcSSabAwQuUy+b5+D15GLRQhAGkNksqYF+/E3N6vlRZpVpaEVZz/mkLPUDcFaU6KOsAvEEmiYI+L2sXt5ENpvLV95yHBzLwrFtTLe7pFtjzQfZnEXfYJR9XUMIIVi5tI7aqgBmmS/5cqbIInesXD6zrczeI4qyGAhNA6GBnDAiarpK8sNajWEcRdc1TEPHpQFWDpzxRC0pKZ+Z4iOi8TTb9/aRzlqkMjle3tVDKl3e9ael4+AOhycFXG9NXcmWOyiKMrOEpmF4PGhuN5rLheH1qeVLc01AWQbeiRxHTlrKBNA3GCUUKL+lENJxkLZNLh5HGAbhlatJ9vUipYOvvgHdo9ZnKspCJjRtys04ZpsKxFMQQqC7XFgT5gCFppGLxdDdrnwmXRkMP2qaoCLooXewOBgHyzAIQz4QF7Y4zGYQuk6gtRWh6Whluoe1oiwmcnz9v+M4aEJDaKXJC1LjaK9BaBqmx4NummiaRi4WJfLKSww+/9yk4uCLWWNtRdEOTFUVPqoqyrN0o50uzqiUto2dTKrhaEVZJBzbIRlPkk6mSSaSZDPZkqwlVmfEr0EIgWPbRPftIz08VChhKMf3rPTW1s1xD0vD7TLYvL4tX9RE5HdpcrnK820jplgWIjR1Jqwoi4HjOGTSxXUkctkcpsuc9bPi8vxGPV5CIG2rqI4wUJIF3vOJ22XgLtPgK6UEKXEsC83lRug68vCG4ZqG7vOVxTSFopQDx5m8v4A6I55jmq4TXLqU9MgwjL9Ahs+HdBzSw8O4KirKdm4wk7XyWyRqWiHTfFGSEuvwkLRt4wpXIsdL3+mmCWpYWlEWBSEEhmlgTViaKEpUO0IF4mMw3B7qN59CajiCk81Xs3n+a18jl0xy+j98FU9V1Rz3sPRSmRzPbe0knck/H62NlbS31Cy66lty/Ex4QgN2NotmmhiqgpaiLCpCCNxuN0IIrJyFpmuFv2ebCsTHIHQdXdcZ3b2bnkceId7dXbis94k/0H7V2+awd6Vn2TZ7Dg4UgjBAV+8ILfXhRRWID2dOvsaFpe2MoiglITSBy+0qzAur/YjnmdTAYFEQBpDluF+xLUkkJ2eNp9K5Ka69MNm2TTSWpG9gBDnF0LNWZjkCilJO8mkh+R/ipdqLQQXi49Ry/vloE4YjNZeL+tNOIxWJ5OtQlwnD0KirDha1CQEB/+IoZiGlJJZIMzA0RjKVZWg4hjBdaIaBZhgYHo8qYakoi5RtO8TiSQYGRhkcGiOdzr72yNgMUj/tj5MrHOb0r36VroceRkqHus0dPP/1bzK8fTsX3fIj/A0Nc93FktA0jZaGcKEGtdtlsGZZw6JJ1rIdh7FoovB3LJ4imczQ3FiFqwTLGBRFmRtSStLpLPF4fmtTbMnwSIy6ujDaLCdlqkB8nHTTxFtbR21HB7tu/Tnbb/opuUT+C3vnT3/Gpk9/Et1VHnt/ukyDlUvqaG+pQcCkdcW27aCVqCLNTLFsBytn4UiJoetkOZKkld8Wc2E9HkVR3hgpJamj1hEDZNI5zMDshkoViN+gkR076XzgwaK2RG8vjmWVTSCG/OYYR+97mstZjMZS9A9FCfo9NNZWLIjiH7btMDISYzSawDR16mrCpNJHKur4vG50Q83iKMpiJoTANAwymeJ8l1LsRT//vyXnmfpTT0EzTZzckRdr+bveWbzMpQw5jkPv4Bj7u/O1mCOjCQZH4mxc3ZzfTnIec6RkdHw4OpezGR1L0NJYTc6yMQ0d08xnziuKsngJIQgEvKQz2XwlQcDjcWGUYNptRn7mCyEuE0LsEkLsEUJ8biZuc75yV1Zy4Y9+QP2pHVStW8vmv/ksyb4+fvfJT5McGJzr7s0Zy3Lo7hstakskM1jzNLPccRyyOYvByBjOUX1MJNN0HRrC63Hh8bhUEFaUMqHrGjXVFdTXhamvqyRcEZg08jcbpn0PQggd+B5wObAOuFYIsW66tztfGW43latX0fGFz9F28UV0PfwoL3zjm4zu2s0r3/8BuWRyrrs4Z3Rt8hyqNk/nVS3bobN7gNGxBOlMFq+neFohFPSqOWFFKUO6rqHp+pTTb7NlJsYMTwX2SCn3AQghfgG8Hdg+A7c9b8W7unnx2/9e1BbZuhU7lcb0ld/uRKaps6y1lu17ewtt1WF/YW9P23bGk57ANPQ5CXKO4+A4EpCMjsULdTkiwzEaGypJJjOkMzn8Pg/BgKdkH0JFUeYH27bJZi0io3FchkFl2I9Rgu+rmQjEzUDXhL+7gdNm4HbntUBbK0LTitYQ13VsRivTzeGFEFRW+OjYsITISIKA303A58Y0dXI5i+6+EXoHxzCNfMCuCHkxSjjkazsOifH1wQG/B23C2bvtOHQfitBQFyZcEVhwGd+KosyMVDrHwe4jU4wjY3GWLZ395Zkz8ZN/qm+sSeVIhBA3CiG2CCG2DA4u/LlUVyjEGf/4VdyVYQAaTj+NZW+7il0/u530yMgc925uGIaO3+umramKqgo/LtNASsnQSJye/lEcR5LJWuzY20suZ896f6SU5CybbM7CsR36B0eRUpJIpgkGindN0jSB1+NG1zUVhBWlDNm2w9BwtKjNsh3S6dnff34mzoi7gdYJf7cAh46+kpTyh8APATo6OhZ8sV7T66XxrLdw8dqbSA4MEnllK4//1V+TGR4hPTTEpk9/qiyHqI9m2w5DI/FJ7WOxFF6PC8uy88PFAgxdm7GF8/k1gVl6Dg0jpaS56cjmHI4jGRmN0dJYTSKZRghBMOhTQ9GKUubEFOeVC2XTh2eBlUKIdqAHuAZ47wzc7rynGwZ2NssjH/14UXvn/Q9ywsc+qgIx+TPNgM/NWCxV1O73ucnlLPZ1DTEaTaJrgtamKqorA296yNqybOLJNMlkhuqqID29w4V5aU3TEOLIfg2JZAZNE9RWh1UAVhQFXdeoq60gfjBdaHOZBh737O+0Nu1ALKW0hBB/DtwP6MDNUspt0+7ZAqG73JPmin31dWp4c5ymaTTVVzISTZJM5Yd46mtCeFwm/UNjjEbzWea2IznQHSEU8CIdGI0miCcz1FQG8HpcaJrAsvPJVrom0HUNy3YYGUsgHYeqcJDegRESyXxlnIqQH3vCsqThkTj1tZUMRaJYto3P66amqkIFYUVRCtwugxXtDYxFk5imTsDvLck64hmptCClvBe4dyZua6Ex/D7Wfvg6tt90CwCaaXLSZ/6STDSKMAzcodAc93DuuV0GJ6xqLpS+PDz8fPRZMuSHlPcc7C8E1MhInJXt9TiOpLMngpQS09BY2d7Iqwd6x7OgIRT0FY6BfIa0YeiFhfmxeAohoKWpurC9mQrCiqJMpGkabpdGXU1FSe93fpc8WgBcgQCrrnk3Sy67hOi+A3hqqnn1v39J5/0PsuHjN7LyPX+K4fXOdTfnnMs0YMIIj+M4BANe4sni2q5CiKKACvkhowNdA4WSkx63i5FoohCEpzI0HKOxvpL+gVGyOQu3y6SmKlSScnWKoixMOcsmlc4SS6SpCHrxuMyFc0Zc7lzBIHY6zYvf+XeSff1IO38Wtv2Wn7D0yreqQDwFTdNorA2RSKaJxvMJUy0NlVMmSzC+P2hxW/HfqXSWgN9DPJEu/J3LWbS21AD51P5SfKAURVmYLMump2+YvsF85nQX0NZURUNthdp9aaGQUpI41FsUIJxcDvk6Z23lzjQNVizNDzsL8me+jpQEfO6iM+XDFW4Oz/nGk2maGioZGokVzor7h0ZZubSRZCpLMp0hFPDhdhslXausKMrC5TiyEIQP6+4boaYyiMulAvGCYHg8NJ9zNj2/+32hreWiC0ATOLaNpgLClI5eKK8Dy5fUE40nSSSzVFX6MQ2dFUvrOdg9RDqTI+DLV71a2d7IyGgcR0qqw0F0XaMi5KMipLLVFUV5Y+Tk8hclO5FSgXiGuEIhNn/ur6k9eRN9Tz1D7UknUrVuHb/7xKc45Uufp3LtGnRz9tPgFwPT1KmuDFJdeaTNMHSWL60HKRGaKJzp1teG56iXiqIsJpqmEQ75Cis5AGqqg2j67K+AEZPm3kqgo6NDbtmypeT3WwrZaJSD9z1A31NP0/fU00jHwQwGuez2W/HW1Mx19xRFUZTXkMvZDI3EiMZTVFb4qazwz1h5SyHEc1LKjqkuU2fEM8zO5Xjh375V1JaLxbBS6dc4QlEURZkPTFOnobaCuupQSWvOq4WUM0zTdSrXrilqM/1+DK9njnqkKIqiHItl2UTjaXbs66Orb4RszirZfatAPMPc4TCn//2XCbTmy2+7K8Oc9ndfZnjnLtLDw3PcO0VRFGUqY/E0f3xxH129I+za38/TLx0gky1NMFZD07Mg0NLCBf/5PTJjYyT7B3j1v39J3x+fIrxyBed8+5t4qiqPfSOKoihKSWRzFns6i3cFTGVyJFIZ3K7ZD5MqEM8CIQQIePILXyJ24GChffTVPWRGRlQgVhRFmWfmcncANTQ9i6asEqU2g1AURZlXXKbBirbaojafx4Xf6y7J/atAPEvc4TDrPnJ9UVt49SrMgB87m5ujXimKoihTCQU8vOWkZSxpqmLNsgZO3bikJMPSoIamZ43QNBpOO5WLbvkRB+69j0BLM5WrVvK7T32GNe9/L83nnYMrEJjrbiqKoijjDENnaXM1bpdR0q1sVSCeRa5ggPCK5dRu2sieX93Bi9/6DkjJs1/9R2pO3KgCsaIoyjyQyVps29PHwUPDuF0GJ61toaZy5op5HIsamp5luWSSXT+7ncHnXyjaEGJk16457JWiKIoC+S1Z93dH2NcdwXYkyXSOJ17YTzZnl6wPKhDPMsPrpebEjZPawytWzEFvFEVRlIlylkPPwNik9pGx5BTXnh0qEM8y3eVi9fvfWwjGmsvFCR+/ESeXIx1RBT4URVHmkqFrVIYm7xkf9JcmYxrUHHFJeKurOfOf/5FcIkk6EqHroYd54IMfLhT+8FRXzXUXFUVRypKua6xZVs/gSIJYIr8P+solNXjcpdstTwXiEjEDAXb85FZ23/5fhbZ4Vxf9W7aw5NJL5rBniqIo5c3ncXHeKcuxbQkCDF3HZZZuD/l5E4hzuRzd3d2k0/N3lyKPx0NLSwvmm9hXWDoOqUhkUrsanlYURZk7maxF31CUQ4NR6quCNNdXlDQIwzwKxN3d3QSDQZYuXVrS9VvHS0pJJBKhu7ub9vb2N3y87nKx6j3vpuuBhwptmmnSfO45M9lNRVEU5TjlLJutr/ayvyd/QtTTP0Z/JMbm9S24zNKFx3mTrJVOp6murp6XQRjy9aOrq6undcYeWrqE87//XRpOP43m887h3O9+m86HHyGybTu5ZOky9BRFURSwLIcDh4pHJXsGxrBsp6T9mDdnxMC8DcKHTbd/pt9P7Umb8DU2sveOO3n6K39PsrePrUJwya0/Jrxi+Qz1VFEURTkemhDYE2o8jO/ZU9o+lPj+5rXrr7+euro6TjjhhFm9nwP33MvOn9xKsrcv3yAlr/7yf3Ds0i0gVxRFKXemqbG6va6obXlrDYZe2jliFYgn+NCHPsR999036/fjnmIbRE9VFUJTL4eiKEqpGLrO8tYaLnnLak5Y0cA5HctZu6wes8TJWgv2m/+uZ/qi1ee+AAAgAElEQVQ450tPsPITj3DOl57grmf6pn2b55xzDlVVs7+mt/mcs/E11Bf+dleGWfb2q3Cy2Vm/b0VRFCU/PzwWS/HSrh5ePThIS0OY6gpfyXZcmmhezREfr7ue6eMLP99JOpufUD80nOELP98JwNtObZjLrh0Xb3U1F970QyJbt2Gn0gTbWnnmH/6R6nVrWf2+a3GHw3PdRUVRlEUtmc7y0FO7C1sAdPaOcMmZa/B7XSXvy7TOiIUQfyqE2CaEcIQQHTPVqWP5+l17C0H4sHTW4et37S1VF6bNW11N1Zo17Pr57Tx0w40MPvc8O2/9GV0PP4p0SpuxpyiKUk4cR7L74ODEfXiwHUl33+ic9Ge6Q9NbgXcBv5+Bvhy33uHMG2qfrwaee57R3a8W7crU+eBD5OLxOeyVoijK4iYEU25xaBhzM1s7rXuVUu6QUpZ8P7/GqqmLcb9W+3wVal86qa1y1Up0j6fkfVEURSkXQghWtNUUBV6Py6CptmJO+rMgk7U++7bleFzFXfe4ND77tumtw7322ms544wz2LVrFy0tLdx0003Tur1j8Tc20H7VlYW/g0vaWP2B96G7Sj9HoSiKUi5s20ETgovPWM25HcvpWNfChWeswuOem7SpY96rEOIhYKoMqC9KKX99vHckhLgRuBGgra3tuDs4lcMJWV+/ay+9wxkaq9x89m3Lp52odfvtt0/r+DfKHQ5z4ic/wbobPoydyaC7XIzsepVcLI6nphp3KFTS/iiKoix2mazF3q4hdu0fwJGS9uYq1q9onJNs6cOOec9Syotm4o6klD8EfgjQ0dEhj3H1Y3rbqQ0LIkP6WFyhEIbPR9dDD/P0V/6h0L7+ozew6pr3YPp9c9g7RVGUxSWezLB9b3/h733dw1SH/SxpmrvtaBfk0PRikxkd44V/+3ZR245bfkIukZijHimKoixO/ZHYpLZDg1HsEteXnmi6y5feKYToBs4A7hFC3D8z3So3clLQdSwLaVtz1B9FUZTFqaYyMKmtviqAps3dXgfTzZq+Q0rZIqV0SynrpZSXzlTHyonh9dJ64QVFbVXr16vsaUVRlBkkpSTgc3HmSUsJBfKrbJrqQjTVhed006EFWVlrsTH9fjb95acILm2j94mnqDlxA6uvvQbT58WxLDRDvUyKoijTkc1a9EVivHpwEMPQ6VjfisdlYhhaSfcenor6hp8nPJWVrP3gB1j+jneQSyWJ7HgFaVkEmlsJtS9TS5oURVGmITKW4JlXOgt/P/rMXi47a82cB2FQyVpFurq6OP/881m7di3r16/n29/+9rEPmkH5M1+H0Z3bkLkcSEm8u5PM6EhJ+6EoirKY5CybvV2RojYp5ZSJW3Nh7n8KzCOGYfCNb3yDk08+mVgsxubNm7n44otZt25dyfqQigxNbhscwFtbN6dzGIqiKAuVJgR+z+RRRZ/HnIPeTLZgA/HergjP7zhEIpXF73Vx8tomlrdWT+s2GxsbaWxsBCAYDLJ27Vp6enpKGog9ldXEOw8Wt1VXqyCsKIryJuUsm9XL6ggE3OzaP0A6Y1FV4SMc9M5114AFGoj3dkV48qWD2Ha+LkgileXJl/LBa7rB+LADBw7wwgsvcNppp83I7R0vVyiEv6mZxKEeALz1DXgqq3EcByGECsiKoijHyXEk0XiaZ145SDSRob46wHmnrCBnOXg9Bh6XOiN+057fcagQhA+zbcnzOw7NSCCOx+NcffXVfOtb3yJU4jKTustFeOVqQu3LAYllS0ZjKTQtQyDowzB0FYwVRVGOQyZn8fvn9pLN2QD0R+K8uLOHUze0zYskrcMWZLJWIpV9Q+1vRC6X4+qrr+Z973sf73rXu6Z9e2+GZhhoLheJjF14TI7jEIsmcJxpVwdVFEUpC5ZlF4LwYf2RGPY8+x5dkIHY7516Kc9rtR8vKSU33HADa9eu5TOf+cy0bmvaJFi54spaUsr8BYqiKMoxuU2D6nBxvf6KgHfejSouyEB88tomdL34idR1wclrm6Z1u0888QS33norjzzyCJs2bWLTpk3ce++907rNN02APsXG1TC/3kCKoijzTc6yGR1L0t03wgnLGzhn8zJ0XcPtMjhlQyueOdxpaSrzqzfH6fA88ExnTZ911lnjZ51zT9M0AgEfsWgcx5EIAf6Aj5FoEo/bxO0yMKcM1IqiKOXLth16+0fpHRwDYHA4RnWln8vOXI0QYk63O3wt869Hx2l5a/WMZUjPV7quUVERxJGSbM5i295+Dg3k31yb17fSUBOad0MsiqIoc8l2HPqGokVtkZEErY3V8zIIwwIdmi4XQgg0XSNn2Tzy9KuFIAywbU8f2ZzanUlRFGUiTQg87vmxLOl4zc+fB0qRqRL8LMtmnoyiK4qizDnLskmmsiRTaZY2V5PJWezrHATyWx/qc7jN4bGoQLwAGLpG0O8mlsgU2toaK4knM9iOg9s0MNR8saIoZcqybfoGRokn0gCMjiWprgqyrK0GXdMIBrzz+jtSBeIFwO0yOG3jUvb3RBiNpqivDuL3uXjm5YM4UnLKhiXUVQXUfLGiKGVJOrIQhA8bGYnTvrR+QSS1qjniBcLjNlm9tI4T1zQzOBLn2Vc6ccbHprfv6Z20aF1RFGWxk1Ji2/nyv8GAp/gyFs5iTxWIJ0in05x66qmceOKJrF+/ni9/+ctz3aUimqbhOJLB4XhRe86ycRyHnArGiqKUCcdxSKUyDA+PMTwcpSLoo762onB5VWUAbR7PC0+khqYncLvdPPLIIwQCAXK5HGeddRaXX345p59++lx3rcA0dPw+F4nkkXKerQ2V7O0aIpHKsmFVE74ptvtSFEVZTCzLJhpNFP6Ox5OEw0GqKgP4vG48HhNNWxjnmgs2ECcHB4l3deJkM2guN4HWNny1tdO6TSEEgUAAyNeczuVy827e1e0yOOPEdvZ1DTEWT1NfHcTndfHcti6klDz7ykFOP7F93q6XUxRFmQnp9OS9BTKZLHU1FVNce35bGD8XjpIcHCS6fy9ONp9F7GQzRPfvJTk4OO3btm2bTZs2UVdXx8UXX1zybRCPh8dtsmZZPZvWNDMwHGfL1s5CRbBYIoNtO+QsNUytKMriIqXEzuXIZTL4fW5CweI60uY82lHpjViQgTje1QmOU9zoOPn2adJ1nRdffJHu7m6eeeYZtm7dOu3bnA2apiGEIBpPFbWbhkY6m+P5bV2MxVLYtvMat6AoirJwSCnJpTNY2RyOZWNlsrhMA/d48Q7TNHC7F+a03IIMxIfPhI+3/c0Ih8Ocd9553HfffTN2mzPNZRqctLalkJCgCcG6FY3s744wOBLnD8/vI6OqbymKsghIKZFHnYDZlkVFKEBNTZhwOIiuL8iQtjADseZyv6H24zU4OMjo6CgAqVSKhx56iDVr1kzrNmeTpgmqKvxccNoqzu5YzlmblzE8mqB3MF9nVUpJ/1CMTNYik1UBWVGUhUU6DnYmjZVIgG2jTzH0LAQYhr5ggzAs0GStQGsb0f17i4enNY1Aa9u0bre3t5frrrsO284vB3r3u9/NlVdeOc3ezi5d19B1DZeps31vH119o0WXG4bGUy/tRwjByetaCfim92NFURSlFKTjYMVjSDuf7+JkM+g+3/gyzvx3v2Ga+Ui8wC3IQHw4O3qms6Y3btzICy+8MBNdLDlN01jeWsOhgbFCcY9QwIPHbRZKY27Z2skZm1RGtaIo85OUEmlZ+UocQisE4cPsdBrDHwDbQTd0xHiuzEK3YL+RfbW10w68i43HbXJOxwqiiTS6pmHbDi/t6C5cHk9myGQtdu7vp62xEr/Xjcuc/+XfFEVZ/BzLIheLkYrkV794amox3B6cTHHpSqFpmMaCDV1TWriD6sokYnz7r7qqIH6vi5d29ZCeMDfs9ZgkUhm6ekd44vl9DI3EC8ueFEVR5pKdzZDs70VaFtKySPX15r+fJhTl0D3eRTEUfbRpBWIhxL8KIXYKIV4WQtwhhAjPVMeU6XGZBpvXt2KOn/G6TJ0Nq5rY1x0pXGf3gQESyQw9fSMkU1ksW609VhSlNOxMhnhPN8M7tpMZHcGZYoVHNhbF8PnQXG6MYAjNNBfFUPTRpnt+/yDweSmlJYT4Z+DzwN9Mv1vKdGmaIBz0cm7HCuzxDY1f3tXDyFiycB0hIBpPs69rCLqGWLeikaqwHyklQohF+YZXFGXu2dkMgy+9QHZsDIB4dxdV69Zj+ANYiSO19A2vF810oZkLc33w8ZrWGbGU8gEp5eGfMU8BLdPvkjJTNE3D4zbxe10YuphUbWtZSw1DI7HC3/u7h0ils3QeijAYiarqXIqizAgrmWR4+zZ6//A4qcEBnFyuEIQPG9u3D1foSHlK3evF9AdK3dU5MZMz3tcD/zWDt6fMILfL5LSNS+iPxIglMjTXVTAaTTEWO5IIYduSTNYiFk8Ri6cYiyVZ2lKLpgmkzM9BL+S1eoqizD47l8NOJUFouIJBrGSSA/f8hszwMADD27bScvGluCsryYyMFB2ru92Elq0A8klZ2iJLynotx3yUQoiHgIYpLvqilPLX49f5ImABP3ud27kRuBGgrW16631nk23bdHR00NzczN133z3X3ZlRbpdJW2MVANmcxZ6DA0WXN9aFiE0omZnO5LAdydBQ/perYehUVQXRdf1IhRs1hK0oZevwNNZhuXic7kcfof/pp3AFQyy7+mo8VdWFIHzY4HNbaDjzzKJAXLF8ObrbXZbfJ8cMxFLKi17vciHEdcCVwIXydVJwpZQ/BH4I0NHRMW9Tdb/97W+zdu1aotHoXHdlVrlMg42rWzg0MEoilaWuOoipa3T1RoqvOOElzW87liQU8mFls0jHQTcMDNNEaFpR+TmxQLYfUxTl9UkpcbI59Al1nK1UmmR/H3t+dQeuihDL3nYV7qoqBp59hp5HHs5fJ5Fg2/f/g81f+NKk7weQuEMVVK1bTzYaxd/YiOEPlGUQhmkOTQshLiOfnHWulDJ5rOvPpIP3PcAr//kDkv0D+Orr2PDxj7HkskumdZvd3d3cc889fPGLX+Tf/u3fZqin85fLZdDWVI2UEk0TjEWLX8JQwDtpnjiXs3Bsu/Chsi0LhEA3DOxEAmnlELqeX3R/+MPnODi2haYbCF0vBGnpONjjW03qrsnJGI5jI8TiWLCvKDNFOs5r/tA9+gx1IseysNJpTJ9v0vGZ0VHsbA5N13BXVhYuT4+McOjxJ+j741M0nnkGjWeeiacyTLy7mwev/0ih4MaeX93BJT+5hcEXX5zU13h3N/7WNuIHDxTa6zafguH3YwYC0Pxmn4nFY7oD8N8F3MCD4y/+U1LKj0+7V8dw8L4H2PK1f8ZO5ytGJfv62fK1fwaYVjD+9Kc/zb/8y78Qi8WOfeVFIr9hRP6DGwx4WdneQCyexusxcbtMIpHihAq3y5y09tixbTRAWjkApG2Ti0UxgiFysRiJQ+NFRYQg2LYUw+fDyeWIH+oh3nkQ3eWmct06TH8ATdex0mnSkSGGt27FXVVF1br1mH5//ralJDs2Ru8fnyQ7NkbzOefiqa5Gd+dLd2ZjcWKdnez/zT1ULFtK64UX4KmuLvQ1PTzMocefYHjHDpZefhnB9nbcoSCQX06RGhpi752/xvD4aL/yrXhqqtH0/BKwzOgowzt20vO7x6k/tYPak07CU3lkxV5qcJAD995HKhJh+Tvejq+xAdPrzfcrHifR08PeO39DaEkbrRdfiLeoXyP0Pf0MQy+/QtvFF1KxfDnuilC+X7kc6cEh9t55F0LXWPb2q/DU1KCPz59lxsYY2bGTrkcepe7kk6g/7VQ8lZVH+jU0xMH7HyB5qI9l73w7/sZGTH9++7hcIkmir5d9d96Fv6mRtosvxlszoV8jI/Q/8yyDz79AywXnU7lmNe6KfEKNbVmkh4bYd8evcRyb5e98B97aWnTTHO9XlLE9e+h88CGqN2yg8YzT8VQd6Vc6EqHr4UeIHeyi/e1X4m9qxhXIv865VIpkXx977/g13upqlr71cry1NYVjMyOj9D/3HP3PbKH53LOpXr8Odzj/WjiWRToSYf9v7sFKp1n+jrfjra0pvEcy0Six/Qc4cN8DVK1dQ9NZZx7Vr2G6Hn2Msb37aL/qCoKtrbiC+aQhK5UiOTDA3v+9E1dFBe1XXoG3proQuDKjowy++BK9Tz5F01lvoWbjhkK/pOOQGopw4J57yUZjLH/X2/HW1WEU3rsxYgc72X/3vYRXrqDl/HPxVFUVvXe7HnmMkZ27aL/ickLLl+EO5d8jVjpNcmCAPb/8X0yfl+Xvegee6urCHGs6Msye//kVkW3baD7vPFovOK/Qr2R/P0/97d8x9NLL+BrqOe3vvkzVurXY6QwvfvM7dD7wIADdjz7GkisuZ9On/pwdP721qOpVdmyMgeeeo2rdOuKdB5nIW1tLeOVKovtbSQ8PU7l6Da6KCvUDewIxFwUdOjo65JYtW4raduzYwdq1a4/r+LvfcTXJvv5J7b6Geq6881dvqk9333039957L//xH//BY489xte//vUp54jfSD8XOsdxyGYtxsbiOI7E7TapqPCTSxdXutF0Hc1xJlXAMUIhRnfvKhre1kyT0NJlxHsPMbz1lUK70DSazz0f3eNhbPduOh84suuVqyLM8j/5E0yfn8zYGFu++g9ko+M/EIRg8+e/QGjJUqSU9Dz2e578/BcLx4ba2znve9/GU1VFemSUP/z13zC8dVvh8o4vfI6lV1yOpuvEOru4//3X4WTzG46bwSCX/uyn+OpqsVJptt98CztvPZIG0XbZJZz8V3+JKxgkNRThoQ/fQGpwqPB4LvzRD6hal3+v9D75Rx7/zF8Xjg20tnLBD76Hp6qKzOgof/y/X2Hg2SOfiU1/+ReseNc70EyT+KFD3H/tB7Az+R+ehs/LpT+/DX9DPXYmy87bfsa2/3dT4dims8/ilC99HndFBelIhIc+8jGSvX2F5+v87/87tZs2ATD44os8+n8+WXiN/I2NXPijH+CpriIzNsazX/0nDj3+h8Jtr7/xI6x533vR3S4Sff3c/973YyXzeQW6282lt99KoKkJJ5fj1V/9Ly99698Lx9ad0sEZ//AV3OEw6eFhHv34nxHr7CpcfvY3v07jGacDMLx9Bw9/5GOFkRdvbQ0X/fgmvNXVZGMxnv/XfysECIA1H3gf667/MIbXQ3JgkPvf90Fy4z+oNZeLS2/7CcG2Vhzb5sA9v2XLP36tcGz1hhM461++hrsy36/fffLTjO3dV7j8jH/8Ki3nn4sQgtE9e3jwuhsKQchdGeaSW3+Mt6aGXCLBS//+PfbdeVfh2OVXv5ONn/g4pt9PamiIB97/ITLjG8sIXeeSW39MxbJ2pOPQ9dDDPPW3f1c4NrxyBed8+5t4qipJj4zw+Kc/y8iuXYXLJ753owcO8MD7P4Rj5RexmIEAl/78Vnx1tfn3/V/9NcPbdxSOXfGnV7PxEx/HsSz++H+/Qv9TTxcuM3w+Lv/vnyMdh7vffnXR51doGlfc8T+8/P3/LHr+AU7/uy/TcNopvPStb5EZyc8J15/xFpZecUXZZD+/HiHEc1LKjqkuW5ATecn+gTfUfjyeeOIJ7rrrLpYuXco111zDI488wvvf//43fXuLgaZpuN0mNTVh6uoqCYcDaJpWOBMDQAgMlwtn/Gy4mCj6EAM4uRxSSuJdXUXt0nHIRsew0mkGnnu26LLs2Ci5WH5tYXTf3iNBGEBKDtyTP/PJjI6y7aZbio6N7t9PajBfMi8XixUFYYDtt/yY7OgojmWx6/ZfFILw4ev3PPa7/P/H4+z+r18WHdt5/4OFIDS8fXshCB9+PNtuuoVcMpnv149uLjo23tVF/NAhAKxkqigIA+y45SdkxvMU9v7qjkIQPnz9g7/N/1DJxmLsuu3nRcceevwPWKn8j6KxffuPBOHx52vb/7uZbCxGNhZj2/+7ueg1SvT2MrYvH4SsVKooCAPsuu1nZOP5AHfw3t8WHj/kRxT2/uoOIH/WufPHtxYdO/DslsL144cOFQVhgG0/upnM6Bi5RIJtP7q5aE4xNTjE8Lbthcff+eBDRcfu/q9fkovn3yPdj/2uEIQBnGw2/9paFpnRMbbfXPweibyytfCY0pHhoiAMsP2mm8mMjGKl0+z4cfGZYGZklIEtzwH50YX9v7mn6Nh9d95FLpmf8ul/+tlCEIb8yNGOn96Gncnm3yM3/7jo2NFX95AeD2jZsWhREAbY8eOfkhkdw87l2HnbzwtBGPLv10OPP55/vlLJoiAMsO/XvyGXSGJnsgwdVV/fSibJxRMgRGE06DBhGAhNsPa6DxRlNHtqqqk96SRcoQpO/PRfcvLffJ6Ov/0y7VdepYLwcViQgdhXX/eG2o/HP/3TP9Hd3c2BAwf4xS9+wQUXXMBtt932pm9vsTi8ZEnXNbTxAuuGy4XL68Xl8eD2ePJtPn9R6Tnd5wcpJy3EN/z56xnjQ7YT6R5Pvta7Prn+9ZE5rcnDWUJQuG+hTTXcJV7rUMRUjZNufNL/TrrpKS8s9EWAmPxRO+Z9v97lE+9vysf1Ov061pCgmNDv1+vTVM+19nrHHosYL/YvisoaHunW67yOYur2I5dr41d6rRHA177twvMhxBt+PoUQr/s6F7+MU7y3EZOvePgyXct3CdAMc4rL84FS041Jx5t+X/5pNg0qj9rqVXe7MP0+TL+flde8p+iy1e+7BjMQwN/YxGW338baD1/Hpr/4FBff/CM81flhdFcohK+hAU9lFYbP95qPXTliQQbiDR//GLqneDs/3eNmw8c/Nkc9Ki9CCDRNQ9OP7H4idB0zVJH/VxFGM000wyC4ZCmG34/QdMxgiEBTC7ppUrl6DZp55MvDW1eP4fVieL00nPGWovvz1tXlAzgQWrYMd/jIfJ7QNJZecRWG242nspITPnpD0bEVK5YX5hZdgSDVGzcUXb7uIx/GFQ6jGQar33sN2oSkMVcoSPN55wD5ob6V73l30bFtl15S+EFRtW4t3rojPwSFrrP+husxfT7c4QpOuLG4X8GlS/A3NQL5oeb6U08p7tf11xXmiFdc/S50j6dwmeHzseSyS/P9CgZYe90Hi45tOf889PF+VbS3429qOnKhEKz/6A24gkFcwSDrP3pD0Ze0v6mJivb2/P14PTSfe07Rba+97gP5BBtgyWWXFX3R6h4PK975TgDcFSHWXX9d0bH1p52K4cv3K9DURHBJ8TLGE268AXdFBabPx/obPlyUUOStq6NyfJjf8HoLj/+wVddeU+hXy3nn4hqf94f80PSqa9+Npuu4w2HWXf/homOrN27ANX6sp6qa8MoVxf366A24K8MYbjfrPvzBoh+Knqoq6jafDOSD27K3X1V07PJ3vQNjfD6+/tRTcE/IKdAMgzUffD+625Xv10euLzo2vHoV7vG5fldo8nv3hI/egDuc/6ytfl/xe9cdDtN0Zv5zZPh8rLj6nUXHnvipP8esqMBdUcEpX/oC/uamwnVP+/uvYIZCmD4faz7wXs7/z++x/qM3cMEP/oNV73lP/nPqcRNobmbDRz/Cqvf8Kd6aGjXnOw0Lco4YZidr+niU0xzxTHEsKz/8OR68IZ90ZWcyWMkEmulCd7sLmdN2JkMukWD01d14Kqvwt7RgTvjCz4yOMrDlWbLRMRrPPAtXuPJIwks8TuLQIQ7eex+h9naazj7zqISXEXr/+BQjO3ex5NKLCba1Fb607WyW1OAQ+379a3SPl/YrJidrjezcRc/vH6euo4PakzYVJ2sNDdH54MOkIxHar7oSX11tIVDnEgkSh3o5cM+9BJa00XLOOYUzCBhPinrqGQZffoUll1xUlIhj53L5pKi77kbTdZZeeQXe2poj/RobY2zvProf/R21J5043q+JyVoRuh95lERvL+1XXYGvoaHwfOYSSZL9fey/6258jY20XnRBcRLZyCiDzz3HwAsv0XL+uYRXrigkazm2TWpwiAP3/BbpWLRfdWU+ca6QrDVGdN9+Oh96hJqNJ1B/6inF/YpE6Hn0d0Q7O1l21ZX5JLLDyVrJFKnBAfbfdTeemhraLr4Qb01xstbgyy8z8OxzNJ1zFpWrVuEOH+lXeijCgXt/i5VKs+ztV+WTtcbfX9lolOjBTjrvf4DKtWtoPOOMSclah/7wBKN799J+xVvxNzcVArWVyZAaGGT/b+7GVRFiySWX4KmpLgShzOgoka3b6P3j0zSdeQZV69ZOStY6+Nv7yMZjLHvb2/DW1mJ4jiRrxbt7OPDb+wivWEHTWW+ZlKzV/8wWRnbvpu3iiwi0NOMKTnjvDg1x4J77MH1eWi+5CG/1xCSyMeI9PYzu3p1PMqypLjwmKSWZ4RGsdBrd5cJVEZpyFYMyPa83R7xgA/FcWSj9VBRFUeaPRZespSiKoiiLhQrEiqIoijKH5lUgnu+b1M/3/imKoigLz7wJxB6Ph0gkMm+DnZSSSCSCZ0L2qqIoiqJM17zZY6qlpYXu7m4Gx4svzEcej4eWFrXlsqIoijJz5k0gNk2T9vH1i4qiKIpSLubN0LSiKIqilCMViBVFURRlDqlArCiKoihzaE4qawkhBoGDx7zi7KoBho55rcWj3B4vlN9jVo93cVOPd2FbIqWsneqCOQnE84EQYstrlRtbjMrt8UL5PWb1eBc39XgXLzU0rSiKoihzSAViRVEURZlD5RyIfzjXHSixcnu8UH6PWT3exU093kWqbOeIFUVRFGU+KOczYkVRFEWZc2UTiIUQ/yWEeHH83wEhxIuvcb0DQohXxq+3pdT9nClCiK8IIXomPOa3vsb1LhNC7BJC7BFCfK7U/ZxJQoh/FULsFEK8LIS4QwgRfo3rLejX+FivmRDCPf5+3yOEeFoIsbT0vZwZQohWIcSjQogdQohtQoi/mOI65wkhxia81/92Lvo6U471/hR535E39TcAAARBSURBVBl/fV8WQpw8F/2cCUKI1RNetxeFEFEhxKePus6ien2nMm9qTc82KeV7Dv+/EOIbwNjrXP18KeViWL/2TSnl11/rQiGEDnwPuBjoBp4VQtwlpdxeqg7OsAeBz0spLSHEPwOfB/7mNa67IF/j43zNbgBGpJQrhBDXAP8MvGfyrS0IFvBXUsrnhRBB4DkhxINTvEcfl1JeOQf9my2v9/68HFg5/u804Pvj/11wpJS7gP+/vTsIraOKwjj+/7AqtIKKYqtVwYUrNxWhKKWrFNEiDYpIXGjRha3QhWu7a3eCXRURqgWVqgs1GqTVKi5cRdSAqLRgFMGYUkGhKhWk8Lm4N/HlZSYZdDLzZnJ+m8zkToYznDtzZu7c97INFvv2z8BkwaZ9y+8S6+aJeIEkAY8Ab7QdywjYDsza/sH238CbwHjLMf1ntk/bvpRXp4E+/qusKjkbB17Jy28BY7nfd47tc7Zn8vIfwBlga7tRtW4ceNXJNHCNpBvbDqoGY8D3ttv+sqfGrbtCDOwEztv+rqTdwGlJX0p6qsG41sKBPHR1XNK1Be1bgZ8G1ufoz0XuSeBUSVuXc1wlZ4vb5BuTC8B1jUS3hvIQ+53AZwXN90j6StIpSXc0Glj9VuuffT1vJyh/QOpTfpfp1dC0pI+BLQVNB22/l5cfZeWn4R225yXdAHwk6aztT+uOtQ4rHS9puOow6aQ+DDxPKk5LdlHwtyM9jb5KjiUdJA1pnijZTWdyXKBKzjqX19VIugp4G3jG9u9DzTOkrw/8M8+FeJc0bNtVq/XPPub3CmAP6XXSsL7ld5leFWLbu1Zql7QBeAi4a4V9zOefv0iaJA0FjuRFerXjXSDpGPB+QdMccMvA+s3AfA2hrZkKOd4LPACMueSzeV3KcYEqOVvYZi73+auB35oJr36SLicV4RO23xluHyzMtk9KekHS9V2cAwCV+mfnztsK7gdmbJ8fbuhbfoust6HpXcBZ23NFjZI25QkhSNoE3At802B8tRl6Z/QgxcfxOXC7pNvyHekEMNVEfGtB0n2kyVl7bF8s2abrOa6Ssylgb15+GPik7KZk1OV32y8DZ2wfKdlmy8I7cEnbSde1X5uLsj4V++cU8HiePX03cMH2uYZDrVvpSGWf8lumV0/EFSx7ByHpJuAl27uBzcBkzvkG4HXbHzQeZT2ek7SNNGT1I7APlh5vnl18APgQuAw4bvvbtgKuwVHgStJwHsC07f19ynFZziQdAr6wPUUqXK9JmiU9CU+0F/H/tgN4DPha/37k8FngVgDbL5JuNp6WdAn4C5jo6o0HJf1T0n5YPN6TwG5gFrgIPNFSrLWQtJH0KYB9A78bPN4+5bdQfLNWCCGE0KL1NjQdQgghjJQoxCGEEEKLohCHEEIILYpCHEIIIbQoCnEIIYTQoijEIYQQQouiEIcQQggtikIcQgghtOgfy/rlMzX9rHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "x = [i[0] for i in racing_track]\n",
    "y = [i[1] for i in racing_track]\n",
    "\n",
    "# Without lookahead\n",
    "velocity_no_lookahead = optimal_velocity(track=racing_track,\n",
    "    min_speed=MIN_SPEED, max_speed=MAX_SPEED, look_ahead_points=0)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax = sns.scatterplot(x=x, y=y, hue=velocity_no_lookahead,\n",
    "                     palette=\"vlag\").set_title(\"Without lookahead\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax = sns.scatterplot(x=x, y=y, hue=velocity, palette=\"vlag\").set_title(\n",
    "    f\"With lookahead: {LOOK_AHEAD_POINTS}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculate distance and optimal time between each racing point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total time for track, if racing line and speeds are followed perfectly: 22.588165653992515 s\n"
     ]
    }
   ],
   "source": [
    "distance_to_prev = []\n",
    "for i in range(len(racing_track)):\n",
    "    indexes = circle_indexes(racing_track, i, add_index_1=-1, add_index_2=0)[0:2]\n",
    "    coords = [racing_track[indexes[0]],racing_track[indexes[1]]]\n",
    "    dist_to_prev = dist_2_points(x1=coords[0][0], x2=coords[1][0], y1=coords[0][1], y2=coords[1][1])\n",
    "    distance_to_prev.append(dist_to_prev)\n",
    "    \n",
    "time_to_prev = [(distance_to_prev[i]/velocity[i]) for i in range(len(racing_track))]\n",
    "\n",
    "total_time = sum(time_to_prev)\n",
    "print(f\"Total time for track, if racing line and speeds are followed perfectly: {total_time} s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Append everything together and save to .txt file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we have list with columns (x,y,speed,distance,time)\n",
    "racing_track_everything = []\n",
    "for i in range(len(racing_track)):\n",
    "    racing_track_everything.append([racing_track[i][0],\n",
    "                                    racing_track[i][1],\n",
    "                                    velocity[i],\n",
    "                                    time_to_prev[i]])\n",
    "# Round to 5 decimals\n",
    "racing_track_everything = np.around(racing_track_everything, 5).tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write to txt file\n",
    "with open(f'optimals_newest_{TRACK_NAME}.txt', 'w') as f:\n",
    "    f.write(\"[\")\n",
    "    for line in racing_track_everything:\n",
    "        f.write(\"%s\" % line)\n",
    "        if line != racing_track_everything[-1]:\n",
    "            f.write(\",\\n\")\n",
    "    f.write(\"]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 2: Calculate Optimal Action Space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the radius for every point of the racing_track\n",
    "radius = []\n",
    "for i in range(len(racing_track)):\n",
    "    indexes = circle_indexes(racing_track, i, add_index_1=-1, add_index_2=1) # CHANGE BACK? 1;2\n",
    "    coords = [racing_track[indexes[0]],\n",
    "              racing_track[indexes[1]], racing_track[indexes[2]]]\n",
    "    radius.append(circle_radius(coords))\n",
    "\n",
    "# Calculate curve direction\n",
    "left_curve = []\n",
    "for i in range(len(racing_track)):\n",
    "    indexes = circle_indexes(racing_track, i, add_index_1=-1, add_index_2=1)\n",
    "    coords = [racing_track[indexes[1]],\n",
    "              racing_track[indexes[0]], racing_track[indexes[2]]]\n",
    "    left_curve.append(is_left_curve(coords))\n",
    "\n",
    "# Calculate radius with + and - for direction (+ is left, - is right)\n",
    "radius_direction = []\n",
    "for i in range(len(racing_track)):\n",
    "    radius_with_direction = radius[i]\n",
    "    if left_curve[i] == False:\n",
    "        radius_with_direction *= -1\n",
    "    radius_direction.append(radius_with_direction)\n",
    "\n",
    "# Calculate steering with + and -\n",
    "dist_wheels_front_back = 0.165 # meters\n",
    "steering = []\n",
    "for i in range(len(racing_track)):\n",
    "    steer = math.degrees(math.asin(dist_wheels_front_back/radius_direction[i]))\n",
    "    steering.append(steer)\n",
    "    \n",
    "# Merge relevant lists into dataframe\n",
    "all_actions = pd.DataFrame({\"velocity\":velocity,\n",
    "                            \"steering\":steering})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5949484259387031"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(radius)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'With lookahead: 5')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize action space\n",
    "ax = sns.scatterplot(data=all_actions, x=\"steering\", y=\"velocity\")\n",
    "ax.invert_xaxis()\n",
    "ax.set_title(f\"With lookahead: {LOOK_AHEAD_POINTS}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize all actions\n",
    "plt.figure(figsize=(10, 5))\n",
    "sns.lineplot(data=all_actions[\"velocity\"], color=\"r\")\n",
    "ax2 = plt.twinx()\n",
    "sns.lineplot(data=all_actions[\"steering\"], color=\"g\", ax=ax2)\n",
    "plt.axhline(0, ls='--', color=\"g\")\n",
    "a = plt.title(\"Speed (red), Steering (green; positive=left)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculate Action Space with K-Means and Resampling each point with normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a240a0a50>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Steering: Find standard deviation so that probability of >10 degrees steering is 5%\n",
    "steering_sd = -15 / stats.norm.ppf(0.05)\n",
    "steering_sd\n",
    "sns.distplot(np.random.normal(0,steering_sd,10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a23f845d0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Velocity: Find standard deviation so that probability of >0.25m/s deviation is 0%\n",
    "# Note: Here, probability is set to 0%, so no noise regarding velocity\n",
    "velocity_sd = -0.25 / stats.norm.ppf(0.00)\n",
    "velocity_sd\n",
    "sns.distplot(np.random.normal(0,velocity_sd,10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(242460, 2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_actions_norm = all_actions.copy()\n",
    "\n",
    "all_actions_norm_len = len(all_actions_norm)\n",
    "resample_size = 1000\n",
    "\n",
    "# Add gaussian noise to action space\n",
    "for i in range(all_actions_norm_len):\n",
    "    v_true = all_actions_norm.iloc[i][\"velocity\"]\n",
    "    s_true = all_actions_norm.iloc[i][\"steering\"]\n",
    "    v_norm = np.random.normal(loc=v_true, scale=velocity_sd, size=resample_size)\n",
    "    s_norm = np.random.normal(loc=s_true, scale=steering_sd, size=resample_size)\n",
    "    vs_norm = pd.DataFrame(np.column_stack([v_norm,s_norm]), columns=[\"velocity\",\"steering\"])\n",
    "    all_actions_norm = pd.concat([all_actions_norm,vs_norm], axis=0, ignore_index=True)\n",
    "    \n",
    "# Take out actions with max speed, so that they are not affected by gaussian noise\n",
    "# We do this because there are disproportionally many points with max speed, so \n",
    "# K-Means will focus too much on these\n",
    "all_actions_norm = all_actions_norm[all_actions_norm[\"velocity\"] < MAX_SPEED]\n",
    "    \n",
    "# Add initial actions to action space (to make clustering more focused on initial actions)\n",
    "add_n_initial_actions = int(resample_size / 8)\n",
    "add_initial_actions = pd.DataFrame()\n",
    "for i in range(add_n_initial_actions):\n",
    "    add_initial_actions = pd.concat([add_initial_actions,all_actions], axis=0, ignore_index=True)\n",
    "all_actions_norm = pd.concat([all_actions_norm,add_initial_actions], axis=0, ignore_index=True)\n",
    "\n",
    "\n",
    "# Display actions shape\n",
    "all_actions_norm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_actions_norm_less = all_actions_norm.sample(frac=0.01).reset_index(drop=True) # sample bc less compute time\n",
    "ax = sns.kdeplot(data=all_actions_norm_less[\"steering\"],data2=all_actions_norm_less[\"velocity\"])\n",
    "ax.invert_xaxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = all_actions_norm\n",
    "\n",
    "# Calculate action space with KMeans\n",
    "\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.cluster import MiniBatchKMeans\n",
    "\n",
    "# Rescale data with minmax\n",
    "minmax_scaler = MinMaxScaler()\n",
    "X_minmax = pd.DataFrame(minmax_scaler.fit_transform(X), \n",
    "                                           columns=[\"velocity\",\"steering\"])\n",
    "\n",
    "# KMeans\n",
    "# remove 2 actions from KMeans so that low speed & high steering actions can be manually included\n",
    "n_clusters = 21-2\n",
    "model = MiniBatchKMeans(n_clusters=n_clusters).fit(X_minmax)\n",
    "\n",
    "# Centroids (interpretable)\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "minmax_scaler = MinMaxScaler()\n",
    "X_minmax_fit = minmax_scaler.fit(X)\n",
    "X_centroids = pd.DataFrame(X_minmax_fit.inverse_transform(model.cluster_centers_), \n",
    "                                   columns=[\"velocity\",\"steering\"])\n",
    "\n",
    "# Add 2 manual actions\n",
    "# Reason: When car starts new episode, it does not start on or direction of racing line, so \n",
    "# it cannot steer enough to get on racing line\n",
    "manual_actions = pd.DataFrame({\"velocity\":[MIN_SPEED,MIN_SPEED],\"steering\":[30,-30]})\n",
    "X_centroids = pd.concat([X_centroids,manual_actions], ignore_index=True)\n",
    "\n",
    "action_space_e = X_centroids.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(data=all_actions, x=\"steering\", y=\"velocity\", alpha=.1)\n",
    "ax = sns.scatterplot(data=action_space_e, x=\"steering\", y=\"velocity\")\n",
    "ax.invert_xaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Note: Action space can be different every time it is computed because of randome resampling with gaussian noise and also because of the random seed with K-Means. Therefore, try out multiple iterations until you are happy with the result*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output as JSON format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>steering_angle</th>\n",
       "      <th>speed</th>\n",
       "      <th>index</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.0681</td>\n",
       "      <td>2.6372</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.2660</td>\n",
       "      <td>1.5084</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-8.7896</td>\n",
       "      <td>2.1237</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0571</td>\n",
       "      <td>3.6474</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.9708</td>\n",
       "      <td>1.8076</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-3.5432</td>\n",
       "      <td>2.3554</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>12.5625</td>\n",
       "      <td>2.2769</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>11.3986</td>\n",
       "      <td>3.1068</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-5.6517</td>\n",
       "      <td>1.4275</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-10.6884</td>\n",
       "      <td>3.5936</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-18.3972</td>\n",
       "      <td>2.2251</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>17.4822</td>\n",
       "      <td>1.4276</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.3677</td>\n",
       "      <td>2.1333</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>9.7116</td>\n",
       "      <td>2.6275</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.5540</td>\n",
       "      <td>3.9854</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-14.4495</td>\n",
       "      <td>2.7518</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-9.3451</td>\n",
       "      <td>1.7503</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-1.4550</td>\n",
       "      <td>3.1014</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-20.0390</td>\n",
       "      <td>1.4739</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>30.0000</td>\n",
       "      <td>1.3000</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-30.0000</td>\n",
       "      <td>1.3000</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    steering_angle   speed  index\n",
       "0          -1.0681  2.6372      0\n",
       "1           5.2660  1.5084      1\n",
       "2          -8.7896  2.1237      2\n",
       "3           4.0571  3.6474      3\n",
       "4           7.9708  1.8076      4\n",
       "5          -3.5432  2.3554      5\n",
       "6          12.5625  2.2769      6\n",
       "7          11.3986  3.1068      7\n",
       "8          -5.6517  1.4275      8\n",
       "9         -10.6884  3.5936      9\n",
       "10        -18.3972  2.2251     10\n",
       "11         17.4822  1.4276     11\n",
       "12          1.3677  2.1333     12\n",
       "13          9.7116  2.6275     13\n",
       "14          0.5540  3.9854     14\n",
       "15        -14.4495  2.7518     15\n",
       "16         -9.3451  1.7503     16\n",
       "17         -1.4550  3.1014     17\n",
       "18        -20.0390  1.4739     18\n",
       "19         30.0000  1.3000     19\n",
       "20        -30.0000  1.3000     20"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Output JSON format\n",
    "action_space_for_json = action_space_e[[\"steering\",\"velocity\"]].copy()\n",
    "    \n",
    "action_space_for_json = action_space_for_json.round(4)\n",
    "action_space_for_json.columns = [\"steering_angle\",\"speed\"]\n",
    "action_space_for_json[\"index\"] = action_space_for_json.index\n",
    "json_text = action_space_for_json.to_json(orient=\"records\", lines=False)\n",
    "\n",
    "action_space_for_json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(f'AS21_newest_{TRACK_NAME}.txt', 'w') as f:\n",
    "    f.write(json_text)"
   ]
  }
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